This is hardly happened in F1. I certainly can’t think of many examples where the same car has been used by different constructors (even in the same team) and they changed the name. Even Ferrari still called their ex-Lancia D50s D50s. When Ligier became Prost the JS45 had already been launched and they kept the name.
Ehm.. no. Sorry for granddad to bust in. The Fittipaldi-team bought the Wolf-team at the end of 1979, and the Wolf WR7/8/9 became the Fittipaldi F7 in 1980. Not a bad car by any means, Rosberg finished 3rd in the first GP of 1980. Then there was also Osella who used an Alfa Romeo-chassis for their 1984 car (I believe).
There are many, many instances of cars being renamed in F1. This was just out of the top of my head. The Dutch magazine RTL GP even has a regular page about it, called Inglorious Bastards.
EDIT:
A quicks search already yielded these results:
Apollon-Cosworth
Was Williams FW03
Merzario A4
Was Kauhsen
Pacific PR 01
Was Reynard
Edited by Nemo1965, 14 January 2021 - 11:22.