Anyoushka \a-nyoush-ka, anyo(u)-shka\ as a girl's name is a variant of Ann (Hebrew) and Anouska, and the meaning of Anyoushka is "He (God) has favored me".
The baby name Anyoushka sounds like Anoushka, Anyshka, Anushka and Annushka. Other similar baby names are Lenyushka and Annouska.