I can see them re-using the same registry number on a new version of a starship, for record purposes. Using an example from my profession, when an old school is torn down to build a new school on the property once occupied by the former building, it is not uncommon for the new version of the school to be given the same name and school ID number, even though it's technically a different school - it's address ID also doesn't change. It seems to make sense to keep the same designation on a starship.
Whereas for record purposes I'd think you'd need
unique registries. It matters whether the maintenance log or upgrade history you're looking at belonged to the original Defiant
or the nee-Sao Paulo
"Chief, why didn't you replace the dilithium before it decrystalized?"
"The maintenance logs said we did just a month - oh. Wrong NX-74205."