Can I rename my link or change the split?

Rename: yes, from your Ambassador tab. The old address stops working the moment you save, so rename before the link is out in the world, not after. Anything it already sold keeps paying you.

The split is an influencer control, and it belongs to the link, not to you. Change it on one link and the others keep theirs, so a link that is already in a video keeps the deal it promised. A change reaches new sales only; nobody who already subscribed is re-priced, and your rate on them stays what it was.