Where do westerners get their "Buddhist" names?

Many western Buddhists have non-western names: - **Jeffrey Block** - *Bhikkhu Bodhi* - **Geoffrey DeGraff** - *Thanissaro Bhikkhu* or *Ajaan Geoff* - **Deirdre Blomfield-Brown** - *Pema Chödrön* Are they given to them when they are ordained as monks/bhikkuni (like *Dances with Wolves*), or are they more informal (e.g. *Ajaan Geoff*)? Just curious.