User Registration Name Fields

After allowing profiles to be viewed publicly on our website, the New User page doesn't show the First, Middle, and Last name fields. The fields show up as un-published and I cannot publish them because only the name field is set to show on the profile (in global CB config). How can I allow all four fields (Name, First, Middle, and Last) to be filled in? I would like all four to be completed and searchable.

What name fields are used is based off the name formatting you've selected within CB > Configuration > General. If you want first/middle/last you need to set the name display to that format.

Is it possible to have both? I am using CB on a school website. Publicly I would like the name field to show as I have it filled in with Mr./Mrs. then the teacher's last name. For the back end of the site and for search ability, I would like top have the full name as well. Any suggestions?

Is it possible to have both?

Possibly; you could display the name with a delimiter field using substitutions. Example as follows.

[cb_prefix] [lastname]