It looks like subagents will do this with curl requests and stuff whatever identifiers it can into the UA header. For instance some requests I made to our webserver:
company-helm-research/1.0 (Claude Code agent run by <my name>, <company> platform team; docs lookup)
Claude-Code-research-agent/1.0 (<Company> platform team; on behalf of <my name>; +https://github.com/<company org>/<repo of project>)
Not great, it even pulled the repo of the project I was in.
That seems to be an attempt to push liability/responsibility onto the end user. As in “it’s not us doing this, we’re just executing the instructions from X”.
Which is quite sensible IMO. Otherwise all the information the site operator would get is "Claude" and they'd blame Claude for damages.