As the house is mortgage free there is no mortgage deed for his name to be on. I take it you mean his name isn't on the Registered Title or Title Deeds.
It depends on him being able to prove a beneficial interest: he could claim a beneficial interest by promissory estoppel, for example.
This is where he treated the property as his own because your friend told him 'what's mine is yours' and he never imagined moving out, contributed to the bills and maintenance as if it were his own and never saved for his own property. He relied on her promise in other words.
Very difficult to prove, but easier if they had shared the house for many years, maybe sold their previous jointly owned home to move in.
He may not necessarily be entitled to half if he is entitled to a share - it may be a much smaller amount.
Your friend needs to get legal advice if they have together for more than a few months.