I didn't think it worked that way in the NFL Hall of Fame. You're just an inductee, you don't get inducted as a "team name here". Of course, if you played you whole, or the majority of your career at one place, they'll say "such and such a team" has so many inductees. But officially, you're just inducted as a player.
You'll see it's all a show, keep 'em laughing as you go, just remember, the last laugh is on you, and always look on the bright side of life!