I'm pretty sure it's not why it was rebranded; the timing doesn't make sense since the rebranding occurred several years after the trademark coexistence agreement.

The curious question though is why 389 was formerly called Fedora Directory Server. From what I've been told by someone who was around at the time (as I wasn't), it's because Red Hat went through a very brief period where it experimented with using the "Fedora" brand as a sort of general "upstream of Red Hat, sponsored by Red Hat" sort of community brand. This was I think quickly rejected as a bad idea but Fedora Directory Server was apparently the one (for a while) surviving example of the experiment. I imagine that the reason for the rebranding was that it was confusing to use the "Fedora" name at a certain point because the directory server project never really had anything particularly to do with Fedora (apart from the connection to Red Hat).