No, you cannot change the domain name of a MemberSnap site.

If you want to create a test site (mysitename.MemberSnap.com) and then transfer it to your own domain (www.mysitename.com), that is not possible with MemberSnap. You can create both sites if you'd like (or create your test and then delete it), however the information from one site will not be available in the other, and as mentioned, there is no way to move it from one site to another without actually creating 2 identical sites.