Anything you want.

State nonprofit corporation laws generally provide specific rights and privileges for voting members of a nonprofit, who have governing powers akin to shareholders of a business corporation.  We regularly recommend a “sole member” nonprofit corporation to give ultimate control to a founder or a group of founders who want assure that additional people on the board won’t hijack the mission the founders envision.  (See Ready Reference Page: “Sole Member Bylaws Can Protect Founder of Nonprofit”)

But the statutes do not prohibit, and our form bylaws specifically do permit (see Ready Reference Page above), the board to create other classes of “members” or “membership” that do not carry with them the right of legal members, particularly the right to vote. 

A lot of organizations simply call such people “members.”  I am a member, for example, of the local public radio and television station, and the art museum.  I get lots of literature, occasional perks on special events or special treatment of “members,” and opportunities to contribute more.  But I have zero rights in the governance of the organizations.  Many people are “members” of a local for-profit gym, but don’t consider that they have any voting rights. 

You can call your members “members” or anything else you want.  You could call them “participating members,” “contributing members,” “non-voting” or “illegitimate” members, “High Flyers,” “Grand Poobahs,” or anything else that fits your fancy.  Pick something, probably more inviting than some of these suggestions, that fits within the purpose of the organization and gives them a sense of belonging.  Just don’t suggest that they have voting rights or the power to throw out the founding members.