Rosinha is a diminutive form of
Rosa, in Portuguese. Just as Carlinhos is a diminutive of
Carlos and Martinha is a diminutive of
Marta, e.g.
The diminutive lexeme -INHO/-INHA (and the variant -ZINHO/-ZINHA) is the usual diminutive lexeme, and it very usual in Portuguese, where the diminutive forms (in names and in words) are more usual that in other languages:
http://www1.folha.uol.com.br/folha/educacao/ult305u2527.shtml
In Portuguese, NH has the same sound as in Occitan (NY in Catalan and Hungarian, GN in French, Ñ in Spanish...)
Lumia
http://onomastica.mailcatala.com