If your main Facebook page is primarily based around your ministry, and most of your friends are also involved in ministry,
then it is not going to be an appropriate environment to build relationships with not-yet-Christians.
It is not dishonest to maintain two different Facebook under slightly different names. Here are some suggestions:
Insert some sort of identifier in your ‘Christian’ profile, eg. Pastor John Smith, Jane 'Saddleback' Smith,
Jack Jones (Grace Mission)
Use a shortened or diminutive version of your name, or a nickname, for one of the profiles.
Married women can run one profile with their maiden name as last name.
Missionaries frequently have a different first-name or even full-name they can use, which has been given them by those in their host country, or chosen by themselves as easier to pronounce. Others take on a local version of their real name, eg. Daoud instead of David, Antoine instead of Tony.
Note that it is possible to edit your name as it appears on a Facebook profile you have already established, though you cannot edit the name of a Fan Page.