she asked the stranger, what his name was.

she said to the stranger: "yo dude, what be mi nameo?"

This is direct speech itself. If you want the INDIRECT (reported) version, it could be: 1.She asked the stranger what her name was. 2.She asked the stranger her name. 3.She asked the stranger her own name. 4.She asked the stranger what her own name was. As the sex of the stranger is not clear, sentences 1 and 2 are ambiguous. They might be understood as " She asked what the stranger's name was". Sentences 3 and 4 would be clearer because of the use of the word "own" which can't refer to the stranger.

ouch it has to be her not his in my answer sorry