Well Panini as stated below had few names and on basis of which it was concluded that his mother was Daksi and his dad was Pani or Panin and he was born in a place Shalatur in the north-western region, now in Pakistan. Refer:

Whereas Pani was also a tribe that existed in the same region but were mainly ancient traders:
The Panis (Sanskrit: पणि : ) are a class of demons in the Rigveda,
from paṇi-, a term for "bargainer, miser," especially applied to one
who is sparing of sacrificial oblations.
They could be related to Panis who were an important tribe of present
Pakistan-Afghanistan region.

More analysis about the tribe Pani can be read here where the author has given references to Rig Veda as well.
Now there are two possibilities:
Either it's a conincidence that the name of his dad was Pani and he got his name Panini from him or
His dad belonged to this tribe Pani and as such he too was a member of this tribe, more so because both his birth place and the region where this ancient tribe mainly existed are very close to each other.
But again question that may arise that Panini was a Sanskrit scholar so how could he belong to a trading community?