Always best to go to the data - I inspected one of the records giving me trouble and found that the data was stored as ?? I recently updated the collations for the database and the users with ?? registered before that.
My confusion arose from the CB User Management page listing users, which evidently gets the first column "Name" from the Joomla users table, not from the comprofiler table fields firstname, middlename, lastname, which is how I have the CB name configured. The Joomla users table was configured with the utf8mb4_unicode_ci so it has the correct data, which is displayed on both Joomla user edit and the CB user list, but not on the CB user edit.
Fortunately there are not too many users who registered before I got the collation of comprofiler correct.
Thanks for your help in solving this.
Richard Brundage