PSN ONLINE ID ASSIGNED ON PS4 ALSO ON PS5?

I wanted to ask whether the online id is assigned on the ps4, e.g. Deutschland123 is the one assigned to the ps5 or are they separate or all together because I want to rename myself but assign them to the ps4 and want to ask whether it is the same with the ps5 ?

If it is taken on the PS4, then of course it is also taken on the PS5 … Both are Playstation Network.