You can even tell the new harness to go find your latest session in the other harness and it works perfectly. You don't even need the name!
In CC, "/exit" will tell you how to --resume <session-id> upon exit. This will eat zero tokens, and it actually does not require an active internet connection.
`claude --resume` will list your sessions, you can copy the title. Codex may just list and grep the sessions files in ~/.claude and filter the one with the name.
I also have the habit of naming my sessions with `/rename`