Your modeling name and your stage name. Which name do you go with? It has to be one that you will stick with. You are branding yourself to photographers and agencies. How will they present you to potentials? And what name will you answer to?
The big thing is not to link your professional modeling life to your home life. Unless you want everyone to know who your friends are, when you are going on vacation, and all of that personal stuff. It is best for you not to have them friended by your modeling community. If you have worked it correctly most will understand why you are doing that. You have to be professional on whatever profile you use for your modeling. No one will hire you if you are going on rant after rant after rant. This is only the basis for a reality show.