Collaborative albums are albums where the owner of an album allows others to add photos or videos. In fact others add "links" to photos that are stored in their own Google Photos. Therefore the photos are also automatically added to the Photos tab in their own account when added to an album.
On a computer
Open an album
Click on 3-dots > Options > Collaborate
On mobile they made it hard to find:
Open an album
Click on 3-dots > Share > Settings for sharing > Collaborate
Add photos or videos
Unlike for example in Google Drive, the owner cannot allow specific users to add items. Anyone having a Google account, access to the album and not being blocked by the owner can add photos/videos.
Remove photos or videos
Anyone can remove the photos he/she added to the album. The owner of the album can remove everything.
Also when someone deletes a photo/video in his/her own account, it will disappear from all linked places, thus also from the collaborative albums.
Edit photos or videos
Anyone can only edit the photos he/she owns. Edits done anywhere will be reflected in all places where the photo can be seen, thus also in collaborative albums owned by others.
Change the order of photos in the album can only be done by the owner of the album.
Correct sorting, even by date can be a major challenge, when some photos have no EXIF data (no "Date taken").
See Change the order of photos/videos in an album
As soon as there are photos or videos of more than one owner in the album, the name of the owner will appear on each photo/video. That means that the photo has been uploaded from that account, not necessarily that this person is also the author of the photo/video. That may be the case when for example the owner of the album adds photos sent to him by other means.
Can the names of the owners be removed?
It is not possible to selectively remove names. The only way to get rid of the names is to replace ALL photos added by others by copies saved to the account of the owner of the album.
Therefore the owner needs to:
Save the photos to his/her own account, for example by adding to another album.
Remove the shared photos from the collaborative album
Add the saved photos again to the collaborative album.
The above can be simplified by adding ALL photos to another (non-collaborative) album. The new album will show the same photos without the names.