I want to invite various people to a shared Google Drive folder but do not want each of the users (except myself) to see the names of the other users with which the folder has been shared.
Users that are explictely included on the sharing settings could see who else has access to the file. To prevent this, create a Google Group, add the collaborators (editors/viewers) to that group then share the folder with the group.
In order to make this work, the group settings should not allow members to see the members list.
You can share your folder by link (eg. not adding users to the list) in which case all users are treated as "Anonymous" to each other (even to you - which is the only possible downside).
To answer the question in the title - only you and people you added to the sharing list are able to see each other's names. Everyone else is just Anonymous.