During the time of the Prophet Muhammad, several of his companions changed their own Arabic names, because the meanings of their names connoted wickedness. For example, someone named Harb ("war") had his name changed to Silm ("peace"), and one named Al-Munba'ith ("one who lies") became Al-Mudtaji' ("one who stands up," i.e. for the truth). So an Arabic name is not automatically an appropriate name for a Muslim.
As a universal faith, Muslims come from many different cultures and speak hundreds of different languages. If one wants to use some of the recommended boys and girls' names from the Qur'an or Islamic history, then of course the name will be of Arabic origin. There are also many traditional and popular Arabic names which are recognizable as Muslim names. But if one would like to choose another meaningful name, one from another language is perfectly acceptable.