How long would you say was a reasonable time to wait after a stray cat turns up, moves into your home and shows no inclination whatever to leave again, before you say "Okay you live here now" and give it a name?
Asking for a friend - they have posted on lost and found local social media and taken the animal to be checked over by the vet and scanned for a microchip and it doesn't have one. It is showing no interest in wanting to leave and they've been caring for it for well over a week now. A neighbour told them it had been hanging around outside for a few days before that as well.