UPDATE After a bit of testing I’ve determined you can rename them in NPC stations and whilst in space, but whilst docked in a citadel I cannot rename any of my ships on any clients, I’ve been able to repeatedly confirm this. It’s specific to ships within citadels. I have reported this via the in-game bug reporting tool as well.
As of the patch today, I can’t rename any of my ships on any of my clients, I simply receive an error message stating “You can’t rename objects you don’t have access to”.
This issue persists across all of my accounts and relogging has not fixed the problem.