Re: my baby girl will be nameless 
there are many accepted translations for Muzna/Muzneh. They all relate to rehmat as they all relate to barish of some sort…whether it be “mist”, “dew”, “puhaar” or simply “rain”.
we went through a very tough time finding a name for our daughter as well…all the names we really liked were already taken in the family.
ultimately we decided on a name that was not unique in the first name “Noor” but unique in the second name “Onaysa”…and even then it was unique because of how we chose to spell it. the commonly found spelling for her middle name is “onaissa” but we decided to spell it with a “y”.
since then we have found several people have appreciated it and named their daughters with the same name.
you will find that whatever you decide to name her, after a few days you will realize that it is the PERFECT name and well-suited to her iA.