I’m not a Picard expert, but I think that this would require sending at least one extra API request per release to retrieve the artist relationships attached to the credited artist(s).
For example, after looking up a release like Brubeck Time with a request like https://musicbrainz.org/ws/2/release/d83320de-1269-3b80-b2c8-525a91e91578?inc=artists&fmt=json, I don’t think that there’s any way to see that Dave Brubeck is an eponymous member of The Dave Brubeck Quartet without sending an additional request like https://musicbrainz.org/ws/2/artist/7bf711e9-4e69-4e08-b6e8-c0cb5805f1e7?inc=artist-rels&fmt=json.
Per @rdswift’s comments on https://community.metabrainz.org/t/possible-to-get-an-artists-legal-name-in-my-file-renaming-script/471702, it sounds like it might be possible to fetch the artist relationships using a plugin. Classical Extras may be a starting point for this. (I don’t see any references to “eponymous” in Classical Extra’s source code or in the main picard-plugins repository, so I suspect that this isn’t already supported.)