They have a plugin ecosystem, one of which is auto-named sessions. I imagine implementing your own wouldn't be too difficult either, if that one doesn't meet your standards of trust.
You could even just make a harness hook in Claude or Codex after installing the Herdr skill, telling the LLM itself to update names on start.
Heck, I think this works via the plugin system?
Look at that: https://github.com/kryptamine/herdr-auto-title
I must say I didn't know this existed. I looked into having the LLM name herdr sessions but found that tabs aren't addressable - the agent doesn't know which tab it's running in to target it for renaming.
The plugin is interesting and the defaults are terrible, but I think I could get what I need here. Thanks for your comment!