There's nothing stopping a client from supporting two different fediverse services at once other then the complexity. I have been thinking about how this might look for quite a while. Imagine you had a minimal posting interface for Peertube built into a Lemmy client that would automatically make a new Lemmy post about a Peertube video you just posted.
I totally agree with all the points you made here. I think coming up with a name that could encompass a-lot of potential fediverse things that dont even exist yet and this is the time to do it before you get much bigger. Badger doesn't feel right to me. One thing I do like with the memmy name is the association with 'meme' so even shortening the name to Mem might work
100% agree