When connecting the source control provider via plugin, you should be able to see the actor names resolved using the “Submit Content” button. I just tested this with UE 5.6 and the Git beta plugin.
If you’re using an external client and Git: As far as I know, Anchorpoint is currently the only one that supports showing actor names in this way (disclaimer: I’m one of the developers). It’s specifically optimized for Unreal Engine workflows.