Basing off of Broly, I’d imagine he’d resemble himself as much as he doesn’t.
Visually, NuBroly’s silhouette vaguely resembles OG Broly, but that’s about it. His backstory is much the same by keep the broad strokes; Broly was born with an obscene power level and King Vegeta basically leaves him to die out of contempt/fear of his power, and Paragus uses a device to control an otherwise uncontrollable Broly to use as an attack dog for revenge.
I imagine Cooler would keep the broad strokes the same. Frieza’s brother, doesn’t like/hates each other, has a 5th form/one more form than Frieza, etc. 2 details that might go is him being a part of Planet Trade Organization or possibly even being stronger than Frieza. Both of those details will be tough to reconcile with Frieza being supposed to be the “strongest in the universe” or the head of the PTO.
Maybe he ends up being Frieza’s younger brother? One who’s just now old enough to make a name for himself?