As a result of this careful attention to character interactions, many of the warriors in the games have attracted a number of nicknames over the last eight years. Some of these are based on names (and titles) used by the real-life historical figures; others are inventions used only in Sengoku Basara. And some are nothing more than in-jokes between fans.
In the west, new fans often seem to comment that it's very difficult to learn who all of the characters are. The nicknames don't help and there don't seem to be many resources in English to help people decipher them. I decided to try to put together a list of the most common ones - partly to be helpful, and partly because I was curious to see how many I could remember all by myself. The answer turned out to be 'a lot', though this list is far from complete, and doesn't even touch on honourifics or the multitude of personal pronouns the series employs.
Firstly, a list of nicknames for individual characters. It's hopefully obvious which of these are official in-game nicknames and which are jokes.
Motonari. A joke based on the age he would actually have been if he were at the Battle of Sekigahara.
Motochika. 'Older brother', but used more like the slang expression 'bro'.
Yukimura. His real-life childhood name.
Bishamonten No Keshin 毘沙門天の化身
Kenshin. Literally 'Bishamonten incarnate'.
Masamune. His real-life childhood name.
Chesuto (or Chesuto Shimazu) チェスト島津
Yoshihiro. From his Xavist baptismal name. Based on a kiai shout, it's changed to the sound-alike name 'Chester' in the dub.
Motochika. This was coined by fans after seeing an unflattering piece of artwork.
Daigoten Maou 第五天魔王
Oichi. 'Demon King of the Fifth Heaven'.
Dairokuten Maou 第六天魔王
Nobunaga. 'Demon King of the Sixth Heaven'.
Yukimura. Sasuke uses this word for 'master' or 'boss' along with a description to address most people. Fans sometimes use it alone affectionately to refer to Yukimura.
Densetsu No Shinobi 伝説の忍
Kotarou. 'The legendary ninja'.
Echigo No Ryuu 越後の龍
Kenshin. 'Dragon of Echigo'.
Masamune. 'One-eyed Dragon'.
Gallop (or Gallop Tachibana) ギャロップ立花
Muneshige. From his Xavist baptismal name.
Kenshin. 'God of war'.
Hideyoshi. 'Conqueror King'.
Mitsunari. It's a type of bird (a shoebill, courtesy of Roni Gotangco in the comments) fans think he resembles, which became a meme.
Hentai 変態Mitsuhide. 'Deviant'.
Tsuruhime. 'Princess Miko'.
Motochika. 'Little Princess', a real-life childhood nickname.
Masamune. Used by the Date army to mean the head of their lands (sometimes translated as 'number one').
Tadakatsu. A portmanteau of 'Honda' and 'Gundam'.
Honnouji No Hentai 本能寺の変態
Mitsuhide. 'The deviant of Honnouji'.
Toshiie. His real-life childhood name. Matsu calls him Inuchiyo-sama.
Yoshihiro. A cute, informal way to refer to an older man.
Joe C. (or Joe C. Kuroda) ジョーシー黒田
Kanbee. From his Xavist baptismal name. Based on Josui, another name he went by in real life.
Kai No Tora 甲斐の虎
Shingen. 'Tiger of Kai'.
Nobunaga. Nouhime calls him Kazusanosuke-sama.
Keiji. A phonetic pun.
Kanbee. A simple contraction of Kuroda Kanbee.
Mitsunari. 'King of misfortune'.
Hisahide. 'Ruthless villain'.
Lovers (or Lovers Naoe) ラバーズ直江
Kanetsugu. From his Xavist baptismal name. Based on his kabuto design.
Maa-kun (or Maa-chan) まーくん or まーちゃん
Nobunaga. 'Demon King'.
Maou No Ko 魔王の子
Ranmaru. 'Child of the Demon King' - obviously, not literally.
Yoshimoto. Derives from the affected way he refers to himself.
Ranmaru. Used by Nobunaga.
Kojuurou. 'Right eye [of the dragon]'.
Mori Boy 森ボーイ
Yoritsuna. 'Forest boy'.
Nankoubou Hentai 南光坊変態
Tenkai (Mitsuhide). 'Tenkai the deviant'.
Nari-sama ナリ様 or 就様
Nee-sama or Nee-san 姉様 or 姐さん
Magoichi. Other characters (like Matsu) are described as 'older sister' as well, but on its own Onee-sama, Nee-sama or Nee-san is usually Magoichi.
Keiji. This rather mean nickname refers to his lack of a job or goal.
Nichirin No Moushigo 日輪の申し子
Motonari. 'Child of the Sun'.
Sasuke. Sometimes Kojuurou or Yoshitsugu instead. It's slang for 'mother', referring to the way they look after their lords.
Katsuie. It's a reference to his bobbed haircut.
Motonari. Because he resembles the plant.
Onigashima No Oni 鬼ヶ島の鬼
Motochika. 'Demon of Onigashima'.
Oni Shimazu 鬼島津
Yoshihiro. 'Demon Shimazu'.
Motochika. 'Little Demon', a real-life childhood nickname.
Nobunaga. 'Fool', from one of his actual real-life nicknames.
Oushuu Hittou 奥州筆頭
Masamune. 'Head of Oushuu'.
Owari No Ooutsuke (or Owari No Utsuke) 尾張の大うつけ
Nobunaga. 'Fool of Owari', one of his actual real-life nicknames.
Shingen. A respectful way to address the head of the house.
Ryuu No Migime 竜の右目
Kojuurou. 'Right eye of the dragon'.
Saikai No Oni 西海の鬼
Motochika. 'Demon of the Western Sea'.
Hideyoshi or Sasuke. 'Monkey'. In Hideyoshi's case it was a real-life nickname. It's part of Sasuke's name.
Magoichi. Used by Motochika and presumed to be her real name.
Sengoku Saikyou 戦国最強
Tadakatsu. 'Strongest in the Warring States'.
Shikoku No Oni 四国の鬼
Motochika. 'Demon of Shikoku'.
Sunday (or Sunday Mouri) サンデー毛利
Motonari. From his Xavist baptismal name.
Sacrificial pawn(s). This is what Motonari calls everyone other than himself.
Suteki Shinshi 素敵紳士
Yoshiaki. 'Splendid gentleman'.
Motonari. Used by Sourin and Xavi.
Shingen. Sasuke uses this word for a general or lord for Yukimura too in Sengoku Basara 3/The Last Party. The word itself isn't character-specific outside of the Takeda forces.
Ieyasu. His real-life childhood name.
Takedagun No Okan 武田軍のオカン
Sasuke. From fans joking that he's the caring mother-figure in the Takeda forces.
Takenoko Hamburg たけのこハンバーグ
Hanbee. It's a joke originating from the Minna Tomodachi Sengoku Basaradio show, 'bamboo shoot Hamburg steak'.
Toushou Gongen 東照権現
Ieyasu. 'Avatar of the Light of the East'.
Tsuruhime. Used by Motochika.
Ushuu No Kitsune 羽州の狐
Yoshiaki. 'Fox of Ushuu (Dewa)'.
Utsukushiki Tsurugi うつくしきつるぎ
Kasuga. Used by Kenshin, meaning 'beautiful blade'.
Wakaki Tora 若き虎
Yukimura. 'Young tiger'.
Motochika's crew, when being addressed by Motochika himself. Literally 'you scoundrels', though pirate phrases such as 'me hearties!' are thematically appropriate.
Yoiyami No Hane No Kata 宵闇の羽の方
Kotarou. Tsuruhime's weird nickname for him, 'the one with twilight wings'. Twilight Ninja in the dub.
Yukkii (or Yukki) ゆっきー
As well as the individual names I've listed above, fans often refer to groups of characters linked together by special 'collective nicknames'. Please note that I'm not referring to BL pairings; this notation is frequently used on sites like Pixiv and Nico Nico Douga as shorthand when describing multiple characters who appear in a single picture/video/story.
This list will never be complete since people make up new groupings all the time; here are some of the most common.
蒼紅 (azure/crimson) Masamune, Yukimura
双竜 (twin dragons) Masamune, Kojuurou
信号機 (traffic lights) Masamune, Yukimura, Keiji
団子色トリオ (dango-coloured trio) Yukimura, Mitsunari, Motonari
紅翠 (crimson/jade) Yukimura, Motonari
蒼紅紫翠 (azure/crimson/purple/jade) Masamune, Yukimura, Motochika, Motonari
伊達主従 (Date lord and retainer) Masamune, Kojuurou
真田主従 (Sanada lord and retainer) Yukimura, Sasuke
武田主従 (Takeda lord and retainer) Yukimura, Shingen
石田主従 (Ishida lord and retainer) Mitsunari, Sakon小早川主従 (Kobayakawa lord and retainer) Hideaki, Tenkai
北条主従 (Houjou lord and retainer) Ujimasa, Kotarou
鉄壁主従 (iron fortress lord and retainer) Ieyasu, Tadakatsu
蒼紅主従 (azure/crimson lords and retainers) Masamune, Yukimura, Kojuurou, Sasuke
保護者 (guardians) Sasuke, Kojuurou (sometimes includes Yoshitsugu too)
関ヶ原 (Sekigahara) Ieyasu, Mitsunari
瀬戸内 (Setouchi) Motochika, Motonari
瀬戸内トリオ (Setouchi trio) Motochika, Motonari, Tsuruhime
川中島 (Kawanakajima) Kenshin, Shingen
東北トリオ (Touhoku trio) Masamune, Kojuurou, Itsuki
東西アニキ or 東西兄貴 (east-west brothers) Masamune, Motochika
東軍コンビ (Eastern army combination) Ieyasu, Masamune
西軍 (Western army) Mitsunari, Yoshitsugu, Motochika, Motonari, Kanbee, Yoshihiro, Yukimura, Sasuke, Oichi, Tenkai, Hideaki
東軍 (Eastern army) Ieyasu, Masamune, Tadakatsu, Kojuurou, Keiji, Ujimasa, Kotarou, Magoichi, Tsuruhime, Yoshiaki
武田軍 (Takeda army) Shingen, Yukimura, Sasuke
織田軍 (Oda army) Nobunaga, Nouhime, Ranmaru, Mitsuhide (sometimes includes Nagamasa, Oichi, Ieyasu, Tadakatsu)
豊臣軍 (Toyotomi army) Hideyoshi, Hanbee, Kanbee, Yoshitsugu, Mitsunari, Ieyasu
前田家 (Maeda family) Toshiie, Matsu, Keiji
前田夫婦 (Maeda couple) Toshiie, Matsu
浅井夫婦 (Azai couple) Nagamasa, Oichi
織田兄妹 (Oda siblings) Nobunaga, Oichi
二兵衛 (two 'bee's) Hanbee, Kanbee
両兵衛 (both 'bee's) Hanbee, Kanbee
友垣 (friends) Hideyoshi, Hanbee, Keiji
三忍 (three ninja) Kotarou, Sasuke, Kasuga
若虎組 (young tigers) Ieyasu, Yukimura
智将コンビ (the resourceful general combo) Hanbee, Motonari
お月様コンビ (moon combination) Masamune, Mitsunari
銀色の堕天使 (silver-coloured fallen angels) Motochika, Hanbee, Mitsunari, Mitsuhide/Tenkai
ザビー教 (Xavists) Zabii, Sourin, Muneshige, Motonari, Yoshihiro, Kanbee
地方領主 (regional warlords) Kanetsugu, Harumasa, Haruhisa, Yoritsuna, Yoshishige, Hirotsuna
For good measure, how about a list of the characters' pen names? In Sengoku Basara 3 Utage, equipping the item 'Oushuu Bukkomi Meyasubako' (奥州特攻目安箱 'Oushuu special attack suggestion box') will cause a cheeky presenter to read out postcards sent in to the popular (fictional) Sengoku-era radio show he hosts. It's easy to guess the identities of the anonymous contributors, so here's a list of their nicknames. There were also four characters who didn't leave a name for varying reasons (Kotarou, Tadakatsu, Yoshiaki and Hisahide).
まぐまぐ (Chomp chomp) Hideaki
雪だるま (Snowman) Itsuki
天下の岩窟王 (This land's King of the Cavern) Kanbee
隠し味は愛 (The secret ingredient is love) Matsu
関白宣言 (The advisor's declaration) Muneshige
エンジェル (Angel) Sourin
一日一善 (One good deed every day) Tenkai
星に願いを (Wishing upon a star) Tsuruhime
Ok, that's all for now. I've skipped a fair number of real-name titles which I haven't seen many people use in fandom, but there must be plenty that I've missed...