If you mean for calling them, i guess this is expected behavior as in this moment you are using android auto from your private profile, so only private accounts are diplayed. But if a work account calls and the relevant setting enables to show that caller ID, you should be able to see who is calling.
This i not verified behavior on my end and just based on the possibilities i know of how the permissions and so should work right now.
But if sharing information from work profile to private is enabled, i would expect it should show them up both ways.
Just 2 snippets out of the MDM we use for a COPE profile:
As said, i have no experience with it in this special case but ever tried installing Android Auto on work profile as well?
@jasonbayton have you ever had such use case and maybe know a bit more?
the only solution right now is, to pair the phone directly with bluetooth to the car itself. most car's headunits have a built-in telephonebook where contacts get downloaded - here, you can find work profile contacts.
this settings should be Enabled for this:
