raysims3 if you click on Identity using the Plumbob in the top corner in CAS it should open up the panel for you to edit the name as well as age, voice, pronouns, etc. Is that not happening? Are you clicking the name options and have you tried the randomiser dice does that not work either? If you're doing that and it's not working there's a fault in your game in that case. That shouldn't be happening. I'd check that your game and console are both up to date. The current console version is 2.19.4.2310 and if you haven't done it before you can check that by selecting Sims 4 on your console homescreen with the menu button (3 lines) and going to Manage Game and Add-ons. You'll see the game version number next to the Sims 4 logo. I'd uninstall and reinstall the game and add-ons anyway incase it's an incomplete installation.
You should just be able to click on either name field to edit the name of any Sim or pet. It works fine for me on Xbox Series X and worked on my previous Xbox consoles too. It works from Manage Households or from any dresser or mirror using Change Sim. As soon as the name boxes open up as I select them the name highlights in green and I can change it. That's how it should work.