Photos on Mac - Find user-defined custom faces from old iPhoto library

You can only mass delete all assigned faces by removing all named people from the People album. This will reset the face detection, but you would have to name all faces again. If is not possible to search for custom faces selectively.

You wrote: "Many of these custom faces no longer and have a name associated with them and instead have "click to rename" in the text section. "

This is the expected behaviour. The face detection algorithm in Photos is different from the algorithm in iPhoto. Because of this, the faces detected by Photos may be in a slightly different position than the faces found by iPhoto or the faces circles you added manually. In that case you have to name them again. You should be able to name many of the faces waiting to be renamed by opening the People Album of a person and using the command "Confirm additional Faces" at the bottom of the album of this person. Then Photos will show you all faces, that might be this person, but need a confirmation.

But you need first to correct all incorrectly assigned face names, there is no help for it. Photos is learning from the named faces what a person looks like, and if some of the faces are belonging to a different person, it will get worsened Photos will make more and more mistakes. Incorrectly named faces have to be corrected immediately.

You wrote: "In the old days of iPhoto, you used to be able to add a "custom face", resize and position the circle over a person, and give it a name. It was a way of tagging people in photos that would then show up in the Faces section. I believe this feature no longer is available in the new version of Apple Photos anymore."

This is still possible. You can add a custom face starting from the Info panel of a photo, while viewing a photo enlarged. What is different now is, that we can only remove custom faces. But it is no longer possible to remove the faces added by Photos. Photos is keeping each h and every automatically detected face. We cannot position it differently or move it. We can only erase the name that has been assigned. All custom faces circles will be showing an x on the circle. These circles we can delete or resize and reposition.

I don't think that will be possible.

See what options you have in smart albums with "person is" filters, and see if anything there can get you close to what you want.