how do you get the "x" session 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`
/resume in claude code.
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!