Is it permissible to mention the names of our mothers or sisters to our friends?

There is no harm in a man mentioning the name of his mother or sister in front of his friends if there is a need for it. The Companions and those who followed them did not shy away from that. It is more complete for a person to refer to his wife and sister as "Umm Fulan" (mother of so-and-so) and to his mother as "my mother" or "my female parent," unless mentioning the name is required.