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Yeah, these are usually called "dimunuatives" in English -- a "shortened" form of an actual name. I think that Russian distinguishes between it as well: уменьшительный vs. кличка. A nickname is...

Wow. These are terrible -- like an even more twisted form of "Joy to the World (the Teacher's Dead!)" This was horribly popular in like fourth grade (set of course to the tune of the religious hymn...

Our Masha sobs bitterly
It means they raped her!??!? :?:

Since this is for you fan website, I think you could also call her "Наша Маша" (Nasha Masha) which means "our Masha!" It's kind of catchy sounding (to me at least).