Look up Dragomir in Wiktionary, the free dictionary.
Dragomir (pronounced Drah-go-meer) is a name of Slavic origin, typical for Bulgaria and Serbia, as well as Romania. It is composed of the Slavic words drag (dear, precious) and mir (peace). It can be translated as To whom peace is precious, i.e. He who cares about peace.
However, the ending mir, found in many Slavic names, has developed from the Old Slavic term *meru which meant 'large, great, greatly'. Thus the original Old Slavic meaning of the name would be He who is very dear or He who is very precious (to his family). The female form of the name is Dragomira (or Drahomíra), Dragomirka and is also very popular.