The origin of the name is Slavic. It means: peace, great, illustrous. Slavon correspondence: Miroslav/ Mirco which translates to "the glory of peace". It is a male name but it is sometimes used as a family name.
May even derive from a popular nickname form in South Slavic (maybe even in other Slavic langs) - with "-če". So any name which ends with "mir" in Slavic names would have as one of their nicknames "Mirče" (at least in Serbian, Macedonian, Bulgarian). It is pronounced "MIR-che".
Perhaps it is a derived name from the Scythian name Mirxas (pron. Mirshas) which might have the same etymology. Scythians were a ancient tribe of Dacians, the ancestors of Romanians, and maybe this is the reason the name persists.