first of all you must know that your exactly spelled name is:
The name Mariuca is derivated from "MARIA" (a kind of Nickname)
The familly name is common in ROMANIA.
In order to help you I need a litle bit more than a name.
For instance: your name was Mariuca OR Maria?
Also city, vilage, the name of your parents, brothers, etc.
Any detail is important.
You can contact the romanian embassy in Whashington DC.
You can find a lot of people with family name Ciobanu in : www.whitepages.ro