Zima is a Russian surname and it means winter but I suspect it's fairly common and thus not very suitable for the name of a royal family.
Zimales means winter forest, but I am not sure if that sounds like a surname to russian ears.
Like many pagan royal families (I have been reading Pindar's odes) Morena's family claims descent from some deity or demigod. I was originally thinking Leshy but apparently this is a demon and not a forest deity.
At some (probably the same time that Christianity was introduced in our world) the Tsar married a Nivkh or a Finn who introduced bear worship, and this was duly incorportaed into the mythology of the Severian royal family.
I could just keep her surname as Sever, since she belongs to the Severian clan and just as in our world the name Russia derives from the Kievan Rus (descendants of Rurikid), so it is with Morena's family.