The micromamba executable is just a symlink to mamba to avoid breaking users who call it as micromamba:

Since v2 they're essentially the same thing. Is there a reason you want only an executable named micromamba and not one named mamba too?

Ahh I did not know that. No, I don't have a preference for micromamba vs mamba, but based on the docs, they are two different things, from my understanding? I generally liked micromamba as it is faster than mamba.

Also, the installation is "weird" in the sense that it creates a mamba file under my user and not a .mamba file as the docs state.

So I guess it's best to just use mamba?

Historically they were different, but these days they're the same thing now (modulo some implementation details that you shouldn't really notice).

Also, the installation is "weird" in the sense that it creates a mamba file under my user and not a .mamba file as the docs state.

That might be from the caveats:

==> Caveats
Please run the following to setup your shell:
  /opt/homebrew/opt/micromamba/bin/mamba shell init --shell <your-shell> --root-prefix ~/mamba

If you had done

/opt/homebrew/opt/micromamba/bin/mamba shell init --shell <your-shell> --root-prefix ~/.mamba

I suspect you'll get the .mamba that you were expecting.

So I guess it's best to just use mamba?

You can use either; it doesn't really matter.