I don't think there is a special reason. Just the language convenience.
Ideally, there would be no names at all. Like a traditional scary story, it would be abstract. "Once upon a time there was a little girl..." etc.
However, with more than 2-3 related characters it quickly becomes messy. There is a three-generation family in the story, plus a young man. The girl, grandma and grandpa are unambiguous. Incidentally, these are normal and common adresses for people in Russian. However, it is not normal to address someone as "man" or "woman". There are not many workarounds that wouldn't be awkward or sound odd in the context. It is common to say "young man", but this designator is already taken by another character, and there is no equivalent in Russian for a woman . Besides, the lack of definite article in Russian makes references a bit more ambiguous and/or repetitive.
Addressing as "father" and "mother" would be ambiguous in a family with grandparents. The easiest thing is just to name them.
 Technically, this is constructed as "young human [masculine]" in Russian, and it is not possible to say "human" (человек) in feminine.