Fallout 4: unknown name (but probably Dogmeat again)
The Elder Scrolls V: Skyrim: Vigilance
Dragon Age: Origins: Dog (you choose his name)
Dragon Age 2: Dog (you choose his name)
Call of Duty: Ghosts: Riley
Torchlight: Dog
Torchlight 2: Bulldog and Papillon
Nintendogs series: many dogs
Megaman franchise and Super Smash Bros series: Rush
Final Fantasy 8: Angelo
Nethack: Large Dog (note: ‘screenshot’ is from web browser, not actual Nethack)
Pokémon series: many pokémon (selection shown may be incomplete!)
Earthbound: Boney
Please Don’t, Space Dog!: Space Dog
I am sure this list is woefully incomplete. Additions are welcome. Thanks to self-critical-automaton and Alex (not on tumblr) for many additions!
Fable 2 and 3 both have dogs in them as well! (And their appearance/breed can change + you can also pick their names)
Fable 2
Fable 3
Hewie from Haunting Ground (lots of puzzles are dependent on how well you direct him. He’s also one of the few ways you can attack enemies in the game.)
Brown from Rule of Rose, a PS2 horror game about a group of nasty pre-teen girls.
Wolf Pup minion from FFXIV: A Realm Reborn.
Sam from Sam & Max (Hit the Road, Save the World, Beyond Time and Space, Devil’s Playhouse) and also Poker Night 2