sure, no problems. if there isn't any coherent name for a strain how else are you going to relate to it than give it a name? Say you have a bag of your homegrown and then you grow out another strain? Just give them new names. It would probably be best not to use "KUSH", "OG" or "HAZE" though.
Just like a lost/found pet. Sure it had a name before but it needs a name whether it's the same name or not is not the issue.