Lisav, it may, strictly speaking, be a 'rule' that a Catholic child is given one 'Christian' name at baptism, but nowadays it is recognised that all sorts of cultural mixtures exist. My son was baptised 'Karim' in a Catholic church, and his second name (admittedly not trumpeted at the ceremony, but clearly stated when asked "What name do you give this child") is Mohammad, after my husband's beloved late father. My husband is Anglo-Iranian, and our daughters also have Persian names, in fact they only have one name each, and we had no difficulty having them baptised either. We gave my son his second name because all the family in Iran assumed he would take his late grandfather's name, but we felt it would be better as a second name, since my husband's family is not active in the Islamic faith, and I intended to bring him up as a Catholic. 'Karim' means generous or bountiful, and is one of the 99 names for Allah or God in Islam.
If you think of how many Catholics there are across the world, there must be many baptisms conducted where the names aren't 'Christian' in the traditional sense.