When implementing Forms Based Authentication (FBA), SharePoint retrieves the tp_title field from the UserInfo table in the WSS_Content* database to display the name of logged in user.
Depending on the method of adding the users to the SharePoint site, this login might appear with the membership provider details as part of the display name.
The easiest way to modify this requires a direct update to the SharePoint UserInfo table (at your own risk).
At every site collection level, SharePoint stores the name in the UserInfo table. The display name is stored in a field called tp_title. Modify that field to the display name that you want, log in to the site, and you will see the proper display name.