I've tried to include all the names Gus has been called, not just the ones Shawn gave him. If I've missed anything, please let me know in the comments.
Peter Panic - 1x03 “Speak Now or Forever Hold Your Piece”
Silly Pants Jackson - 1x05 “9 Lives”
Francois - 1x07 “Who Ya Gonna Call”
Chocolate Columbo & Magic Head - 1x08 “Shawn vs. The Red Phantom
Dr McTock - 1x09 “Forget Me Not”
Earnest Lambert Watkins - 1x13 “Game, Set, Murder”
Gus T. T. Showbiz - 2x01 “American Duos”
Ovaltine Jenkins - 2x04 “Zero to Murder in Sixty Seconds”
Burton “Oil Can” Guster - 2x05 “And Down the Stretch Came Murder”
Debrick Shaw Stillington - 2x06 “Meat is Murder but Murder is Also Murder”
Schmuel Coen - 2x08 “Rob-a-By Baby”
Galileo Humpkins - 2x09 “Bounty Hunters!”
Skooney “U-Turn” Singleton - 2x10 “Gus’ Dad May Have Killed an Old Guy”
Knick-Knack - 2x12 “The Old and the Restless”
Lavender Gooms - 2x13 “Lights, Camera, Homicido”
Fingers - 2x14 “Dis-Lodged”
Tan (later says it’s Tangus) - 2x15 “Black and Tan”
Bruton Gaster & Patty Simcox - 2x16 “Shawn (and Gus) of the Dead”
Fearless Guster & Lemongrass Gogoloab - 3x01 “Ghosts”
Die Harder & Squirts Macintosh - 3x03 “Daredevils”
Ernesto Agapito Garces con y a de Abelar - 3x04 “The Greatest Adventure in the History of Basic Cable”
Methuselah Honeysuckle - 3x05 “Disco Didn’t Die, It Was Murdered”
Chesterfield McMillan (and Wife) - 3x06 “There Might be Blood”
Longbranch Pennywhistle - 3x07 “Talk Derby to Me”
Scrooge Jones - 3x09 “Christmas Joy”
Hummingbird Saltalamaccia - 3x10 “Six Feet Under the Sea”
Step Anthony Wally Ali - 3x12 “Earth, Wind and Wait for It”
Dekwan “Smallpox” Randolph - 3x13 "Any Given Friday Night at 10pm, 9pm Central"
Hollaback Atcha - 3x14 “Truer Lies”
Killer B (Jason), Lumpkin… (interrupted), Slicks (himself) & Fearless Guster - 3x15 “Tuesday the 17th”
Trapezeus Milkington & Sterling Cooper - 3x16 “An Evening with Mr. Yang”
Jazz Hands - 4x02 “He Dead”
Shawn (no relation) - 4x04 "The Devil's in the Details... and the Upstairs Bedroom"
G-Whiz (college), Gus Brown & John Slade - 4x07 "High Top Fade-Out"
Bob Adams, Rich Fingerland, Black Magic, Cheswick & Harry Monroe - 4x08 “Let’s Get Hairy”
Donut Holstein - 4x09 “Shawn Takes a Shot in the Dark”
Ghee(Guy?)Buttersnaps, AKA "The Heater." - 4x10 “You Can’t Handle This Episode”
“Guts”, Old Ironside & Old Iron Stomach - 4x15 "The Head, the Tail, the Whole Damn Episode"
Jonathan Jacob Jingly Smith - 5x01 “Romeo and Juliet and Juliet”
Santonio Holmes & Dion Richmond - 5x02 “Feet Don’t Kill Me Now”
Gurton Buster (Roy) - 5x03 “Not Even Close Encounters”
Chaz Bono - 5x04 “Chivalry Isn’t Dead, but Someone Is”
Chocolate Einstein, MC Clap Yo Handz, Crankshaft, Mrs. Whiddlebury, G-Force & Sher-black-lock - 5x05 “Shawn and Gus in Drag (Racing)”
Imhotep & Control-Alt-Delete - 5x06 “Viagra Falls”
Yasmine Bleeth - 5x10 "Extradition II: The Actual Extradition Part"
Lodge Blackmunn - 5x12 “Dual Spires”
Mission Figs - 5x13 “We’d Like to Thank the Academy”
Radio Star, Gusjay Gupta & Original G-String, aka Crowd-Pleazah - 5x15 “Dead Bear Walking”
Don Cheadle Jr. (Yin) - 5x16 “Yang 3 in 2D”
Tap Man, Watson Williams & Benedict Arnold Jackson - 6x04 "The Amazing Psych-Man & Tap Man, Issue #2"
Suggs - 6x06 “Shawn, Interrupted”
Ingle Woods - 6x07 “In for a Penny”
Brutal Hustler, Barton & Braxton - 6x10 "Indiana Shawn and the Temple of the Kinda Crappy, Rusty Old Dagger"
Fellatio del Toro & Eddie Adams - 6x11 "Heeeeere's Lassie"
Larenz Tate - 6x12 “Shawn and the Real Girl”
G-Whiz - 6x13 “Let’s Doo-Wop It Again”
Hammerin’ Gus - 6x15 “True Grits”
Sh’Dynasty - 6x16 “Santabarbaratown”
Gurn Blandsten & Satchel Gizmo - 7x01 "Santabarbaratown 2"
Immaculate Conception - 7x02 “Juliet Takes a Luvah”
Pootie Tang (Kate) & Nutella (Kate) - 7x03 “Lassie Jerky”
Domo Arigato Mr. Roboto - 7x05 “100 Clues”
Jonas Gustavsson - 7x08 “Turn Right or Left for Dead”
Blue Ivy Carter - 7x09 “Juliet Wears the Pantsuit”
Bill Uvrights - 7x10 “The Santa Barbarian Candidate
Vijay Armitraj, Django Unchained, A Player Named Gus & Burton Goutster - 7x12 “Dead Air”
Mr. Nussbaum & My brother Daryl - 7x13 “Nip and Suck It”
Burton Trout & Bad News Marvin Barnes - 7x14 “No Trout About It”
Lil Wayne, King Mongkut & Gigi van Trenh - 7x15-16 “Psych: The Musical”
The Wizard, Buster (Despereaux) & Busby (Despereaux) - 8x01 "Lock, Stock, Some Smoking Barrels and Burton Guster's Goblet of Fire"
Recap McGee & Trending on Twitter - 8x02 “S.E.I.Z.E. the Day”
Robert Jones & Burteen Gusten - 8x03 "Remake A.K.A. Cloudy... With a Chance of Improvement"
Darnell (Woody) - 8x04 “Someone’s Got a Woody”
Denzel Diggs Underwood Morris Chestnut Washington - 8x05 “Cog-Blocked”
Burton Guster Black-Spencer & Blackstone (Simpson) - 8x09 “A Nightmare on State Street”