Alright now everyone's doing it. Since @coopaloop1234 still thought I was 13 until I posted action pictures a few months ago, I'll make this list from a 2000s kid's prospective. Keep in mind I actually follow hockey and its history so some of my answers will still be older goalies.
Ducks- Jonas Hiller (Gibson if you're a baby born after 2004) And yes really the Hiller/Quick playoff battles were great back in my day
Coyotes- Mike Smith (anger management)
Bruins- Rask (more anger management)
Sabres- Dominik Hasek (they've never had a consistent guy in my lifetime)
Flames- Mikka Kiprusoff
Hurricanes- Cam Ward
Blackhawks- Corey Crawford (carried by good teams, from a kid in Chicago)
Avalanche- Semyon Varlamov
Blue Jackets- Sergei Boobtitski
Stars- Kari Lehtinen
Red Wings- Jimmy Howard
Oilers- Fuhr (who else am I supposed to say? Viktor Fasth or Jeff Deslaurier? ASS)
Panthers- Rubber-Toe Luongo
Kings- Jonathan Extremely Fast
Wild- Niklas Backstrom
Canadiens- Carey Price
Predators- Pekka Rinne
Devils- Martin Brodeur (special shoutout to Corey Schneider when he first got to NJ)
Islanders- Billy Smith (they had 2,000 goalies before Sorokin took over)
Rangers- Henrik Lundqvist
Senators- Craig Anderson (CYA alumn)
Flyers- Ron Hextall (although Hart's going to become to most well known once he goes to prison for sexual assault lol)
Penguins- Marc-Andre Fleury
Sharks- Niemi or Jones or some other guy that was good for 2 seasons
Kraken- Philip Grubauer (6 million for more injuries than seasons played with the team)
Blues- Brian Elliot (was so underrated in the late 2000s and early 2010s)
Lightning- Ben Bishop (for my era but Khabibulin is iconic. Vasy is getting there too)
Leafs- Curtis Joseph (Holy fuck maybe if they won a playoff series once in a while we'ed remember one of their goalies. A sad Freddy Andersen or James Reimer comes to mind)
Canucks- Roberto Luongo (real stud Lu in VAN. Rubber-Toe edition was in Florida when he was stiff and lived on the ir)
Golden Knights- Oscar Dansk (hehe just kidding it's Malcom Subban. gotcha again!) Marc-Andre Fleury
Capitals- Braden Holtby (won them a cup when nobody else could so...)
Jets- Onjrei Pavelec (Hellybellybucykuk needs to play longer and have more success. when I think thrashers to jets relocation I think of Pavelec)