You aren't small! You are just the right size. When do you start the next two groups?
I'm a big "namer" in most things, but we feel that "organic church" "simple church" and/or "house church" are better off without name or membership.
My husband feels like the minute you "name it" then it puts up a wall to those who don't belong. It's a handle, too, that makes it seem "us-them". It begs the question of "if we meet at someone else's house, is it still the same group?"
We try to use all "small letters" when we talk about our faith community, the families that come on Fridays or getting together with our neighbors.
That way, we "are the church" even as we visit an un-yet-saved neighbor, and it isn't a separate entity. It eliminates a good deal of formality, which is the death knell of organic-ness.
I have my computer file called "Little Flock" resources, but that is as close as we come to a name -- and I'm thinking in terms of Jesus saying "little flock" meaning all believers everywhere. At one point we did name a particular meeting, but it didn't take off, so we dropped it.
Many others do use names. Some name the network. I think a lot depends on how strongly you feel about "leaving the matrix". We are trying to be way under the radar for many reasons, such as livestock ownership and home schooling, so the less anybody can name our group, the happier we are.
"We're having people over" is as close to a "meeting time" as we get. So, we can be led of the Spirit about who to invite to be together, and there is no offense. If we had a meeting time and a name it would require conflict resolution to deal with the fact that we felt "so and so" was getting a little too leader-y for our vision.
Sneaky, huh!
We also avoid having to have a "statement of faith" if we don't organize under a name. If others feel differently, they just meet elsewhere. If you have named your group, then there has to be a break-up if the visions don't match. In our lives, we are loosely tied to 4 different gatherings, and 10 different families, and each of us is very free both to follow the Spirit's leading and to challenge one another's leading. In each home, the gathering is shaped by the family hosting it. 1 has teaching, one has Bible leading, ours is mainly worship and another is missions-driven. We avoid being anywhere "every week" so things don't gel into stagnation.
Biblically speaking, too, there was "The Church in Ephesus", but was Paul naming it, or just talking about a location? When Jesus was in Simon's house, was that a church or not? He taught, ate, prophesied and fellowshipped, but Simon hadn't accepted the message yet. So what was that? A very different view of "ekklesia" if you realize Jesus was "modeling the Kingdom" right then!