I think that makes good sense!As long as you know that there is some doubt then I don't see any problem. It can easily be changed if new evidence comes to light.
Apologies if I'm going over old ground.
Taking the relationship - cousin - between the other Giuseppe and Nicola listed on the 1911 census at face value then it would imply that Gaetano & Felice had at least one other brother. Assuming that Nicola is Gaetano's son.
Also on the 1911 census there is a Peter Jommi. He could also be Gaetano's son as there is a possible birth listed for him.
Did he take his middle name and change it to Peter?Yes, that's right.
The Peter on the 1911 census if he's who I think he is was listed as Vincenzo Pietro Donato on his birth record. There was an elder brother also called Pietro who died young.
Interesting my wife is Patricia Ann, when she was younger, Patty Ann, now Patricia (Pat).Can't say with any certainty because that appears to be the only sighting of him.
But people with more than one name didn't always use their first (my nan was Sarah Ann but no one called her Sarah) and foreign names do get anglicized. Also, he was a lodger so wouldn't have filled the census in himself.