duplicating nicknames isn't an issue (I'm excluding NHL teams, since that would be an issue):
- Saints
- Broncos
- Lakers
- Cowboys
- Diamondbacks
- Angels
- Rockies
- Bucks
- Raptors
- Suns
- Mavericks
- Trail Blazers
- Spurs
- Colts
- Rams
BTW, Jazz isn't one of them. Still the most awkward fit of any team nickname in US pro sports.