Nickname can be anything. "Крестик ты мой, я твой нолик, ты - мой удав, я твой кролик"
But Masha is short form of name "Maria" it is a jewish name. But there is old slavic name Милана (at baptism Милица in clavic styly or Мелания - probably, it is from greek name Melanie, that was related like simelar in pronounce, thought it have different roots and accordingly meaning), mean "cute". Colloquially used short forms Лана, Мила, Миленка, Милица, Мина, Миланочка, Миначка, Миланка.
No, Masha is an absolutely different name. I guess normally a guy would use some endearing nickname like "kitten" or something in that spirit.
Masha is short and informal appeal on behalf of Maria. I do not think will be very approach to name Melinda... And what if your guy will talk just Meli?
Slavic analogue of Melinda (and Melanie) is Melania (both origin. from Greek, meaning "dark"), but this name is rare now; it's mostly associated with rural people.
Short/diminutive forms of Melania: Melanka, MilYa (not Mila), Melya.
Note, please: in Russian "Me-" is soft and often perceived as something in between "Me-" and "Mi-" because "e" here (in this word/name) is unstressed.
Masha is a diminutive form for Maria (MariYa).
pet name for her. masha can be mishka mishika or mishmash
