If you want to keep the gist of the Talons, you could always go with the Miami Spurs. It's a proven pro sports team name even though different in definition.
If you like alliteration you could also use Miami Manus, but unfortunately any name rhyming with anus will get you some very colorful trash talk.
Sticking with alliteration but going down the road less traveled, you could also be the Miami Manhandlers [hint: this is a bit of a reach so if you need help you can always search Talon in Urban Dictionary].
If you're a history buff and want some link to Tulsa to remain with the team, the Miami Muscogees. Florida residents are still accepting of using American Indian team names and I believe the Muscogee are linked with the Seminoles. Some fact checking may be required but I believe Tulsa, OK and Tallahassee, FL are both names derived from the same Muscogee word meaning "old town", so moving to Miami from Tulsa is not completely disjointed.
Sticking with alliteration, those who like force of nature names might go with the Miami Monsoon or Miami Mudslide.
Animal lover alliterafficianados might be motivated by monikers such as Miami Mastodons, Miami Minks, or Miami Mambas, but more meaningful members to muse might include the Miami Macaws, Miami Manatees, or the Miami Manta Rays, I mean let's not get crazy and assume the Miami Mandrills or Miami Moose make any fucking sense whatsoever.
If alliteration is not your game, there's about 3 billion other possibilities that I won't bore anyone with any longer.
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