I see that
https://www.learningstrategies.com is currently running UBB.threads 7.5.7
I've done a search through the language files for "display name unacceptable" and was unable to find that exact phrase. Nor was I able to find the word, "unacceptable." in a complete search of 7.5.7.
Expanding further on what Mark has mentioned;
I see that you use a registration queue to manually approve new users. It is possible that the phrase, "display name unacceptable" was entered in the "Decline Registration" section's "Reason" box (@ Control Panel > Member Management > Registration Queue) on your site.