hang one's hat

verb2

1. •
   (US) To reside; to call a place home.

   • But all my ex’s live in Texas And that’s why I hang my hat in Tennessee — 1987
2. •
   To identify with; to be.

   • I try not to make simplistic judgements on people these days. Especially over matters as trivial as where they hang their sexual hat. — 2009