While I've seen the 2 used interchangeably I think the version with the "p" is the anglicized version. In every academic book published on the Habsburgs it's always (as far as I've seen) spelled with a "b" and it's important to note that the modern descendants of the royal line spell it with the "b"

Anyways, the Habsburg family took the name Habsburg after their ancestor, Radbot, built a castle called it Habsburg According to wikipedia it was because he saw a hawk on the castle walls (Habicht is hawk in German) or because in middle German hab/hap means "ford" and the castle was located near one.. I've heard from a history professor (when I took his class on the Habsburg monarchy (ignore the odd spelling mistake on the university's webpage)) the story about the hawk.