I was inspired by the Mario Party series for this. Basically, they're just fun little nicknames that mimicked their personality traits or things you would associate with a pair. I haven't done one for every single character, but I have done quite a few. It's if they're the Impostors, by the way.

Player x Veteran - Best Friends
Player x Captain - One Sided Friendship
Player x Mr. Cheese - Eternal Rivals
Player x Dum - Siblings Unite
Player x Goober - Sane and Insane
Player x Rookie - Total Noobs
Player x Bro - Friendly Enemies (MaryExsists90)
Player x Noob - Unrequited Love (MaryExsists90)

Mr. Cheese x Angel - Two Sides of the Same Coin
Mr. Cheese x Mr. Egg - Omelettes
Mr. Cheese x The Gentleman - Dark Hearts
Mr. Cheese x Ninja - Overmatched

Captain x Dum - Dumb and Dumber
Captain x Stoner - Flying High
Captain x Mr. Cheese - Catchy Icons

Ninja x Mr. Egg - Fast Food
Ninja x Veteran - The Professionals
Ninja x Bro - Quick Wits
Ninja x Sheriff - Sharpshooters
Ninja x Hunter - Weapons Experts
Ninja x PoopyFarts - Language Barriers

Veteran x The Gentleman - Gruff and Tough
Veteran x Captain - Friendly Feud
Veteran x Mr. Cheese - Restaurant Regulars
Veteran x Engineer - Brains and Brawn

Mr. Egg x The Gentleman - English Breakfast
Mr. Egg x Hunter - Poachers
Mr. Egg x Angel or Happy - Sunny Side Up
Mr. Egg x PoopyFarts - Rotten Eggs
Mr. Egg x Ria - Green Shells (MaryExsists90)

Baggy x Blondie - Timid Twosome (MaryExsists90)

Dum x Gnome - Dynamic Duo (MaryExsists90)

BDay x Flamingo - Lovebirds

Any of Mr. Egg, The Gentleman, Sir Clogsworth and Wizard - British Fellows

BDay x Gnome, Rose x Engineer - Awkward Date

Sir Clogsworth x PoopyFarts - Toilet Humour

Blue x Not-Orange - Mischief Makers

Bro x Mr. Cheese - Officers of the Law

If you have any suggestions, put them down in the comments and I'll edit them in.