Editing Pokemon on the 3DS, does the trainer name need to match a Pokemons TID and SID?

[lovejakey]

Hello, I have Pokemon on Alpha Sapphire that I've moved over to Omega Ruby through Pokemon Bank, and I want to change their OT name out of my deadname. What I'm nervous about is whether I'm able to change the OT name of the Pokemon, but keep the same TID and SID values without impacting the legality of them, since I eventually want to move them into Pokemon Home, and into Scarlet and Violet. They seem to pass the legality checker on PKHEX just fine, but I wanted to double-check in these forums just to be certain. Thank you :)