The name "Hampi" is derived from Pampadevi, and this is based on the following reason:

Local Deity: Pampadevi is a local deity associated with the region where Hampi is located. The name "Hampi" is believed to have been derived from the name of this deity, reflecting the religious and cultural significance of the area.

Historical and Cultural Significance: Hampi is a historic and culturally significant site, known for its ruins and temples. The association with Pampadevi highlights the religious and mythological connections of the area.

Linguistic Evolution: Over time, the name Pampadevi may have evolved and transformed into "Hampi" through linguistic and historical processes, as often happens with place names.

Therefore, the name "Hampi" has its roots in the local deity Pampadevi, and this association has been an important part of the area's history and culture. 

So, the correct option is [1].