Aminb did a good job explaining it. Guix is a package manager & GuixSD is the distro.
GuixSD uses the SLiM display manager by default (as Catonano pointed out). The problem is that, since Guix as a package manager installs programs in a per-user basis, the distro has a unique way of adding WM's to the "choose a WM" area of the login screen (I think)
GuixSD (the distro) also completely and deterministically manages your "system configuration" for you. You write out a system configuration file and it generates all the /etc/ config files, installs the "core" packages of your system, the core system daemons, etc.
generally, login managers require a service to be run
And as far as I understand, there is only a service for SLIM available right now
The best route I see is copying the SLIM service, paste it and then edit the pasted version to tweak it until it manages to run a different login manager
You should do all the tests in a virtual machine
there are a couple of desktop envs already packaged, they only need a login manager able to launch them
Right now I'm having troubles with the virtual machines (nothing works ever) but should I solve this, I'd be glad to coordinate an attempt to create a service for a new login manager (it's already packaged, I just don't remember its name, it's the one used in Ubuntu)
recently I had an altercation with the guix people about the user hostility in some guile/guix aspects
But in this case, I'd say there's no hostility at all
Developing new system services is not meant for users
It's for developers
Once the new system service is in place, users can just use it almost blindly
admittedly the guix core dev team people don't use desktop environments, so the support is... not entirely fulfilling
But the standard answer, in this case, is: step in and fix it yourself
On the inadequacy of this standard answer, there are tons of things to say.
But it is what it is. Guix is not more hostile than any other free software projects
If anything, it's less hostile than some other free software projects
In fact it's the only project I ever contributed to