Pakistan has several ethnicities, so you'd have to choose one: the Afghan border has many Pashtuns, the south has Baluchis and Sindhis, the Indian border has Punjabis, and there're some others you hear about less.
The nationality of all those guys together (so, I suppose, the default if you're looking for a group ethnicity) is just "Pakistani". The Urdu for that is apparently Pakistani Qaum, but the qaum just means "nation". You could say "Paki" but really shouldn't: the Brits have been unpleasant enough to them that it's turned into an slur.
"Persian" is an exonym (like calling Zhongguo "China" or Nihonkoku "Japan"). Going really far back, it was a section of the southern Iranian mountains; since the tribe from that area was in charge when the Greeks met them it caught on for Europe. The Pahlavis tried to get people to use the local Irani ("Aryan") but it didn't catch on until the Ayatollah.
It's not like there haven't been Muslim states in northern India, but the last and biggest one before the Raj were the Moghuls. They called their land "Hindustan": you can imagine why Jinnah wasn't keen on reviving it. Besides, a religiously-monolithic republic centered on the Indus valley was a new thing needing a new name anyway.
Not an historian, but I have a question for you
Pakistan where? Indus river valley? Near Iran/Baluchistan? Waziristan?
They could be Aryians (sp?) I guess. The whole Iran/Afghanistan/Pakistan/India border thing is a bit fuzzy in places. We can thank the Brits for thinking borders apply in that region like they did elsewhere.
I would also like to seean authoritative answer to this.
Deleted the thread for being about modern ethnicities in South Asia, not about the past.