Word for "music playing in a mall."

You might be thinking of Muzak:

Muzak is a brand of background music played in retail stores and other public establishments. In 1981, Westinghouse bought the company and ran it until selling it to the Fields Company of Chicago, publishers of the Chicago Sun-Times, on September 8, 1986. Formerly owned by Muzak Holdings, the brand was purchased in 2011 by Mood Media in a deal worth US$345 million. - Wikipedia

It doesn't start with P, but it appears that there is a song that includes the word muzak in its lyrics, and the band name starts with P:

The Sound of Muzak by Porcupine Tree

If you want a term that begins with a P and is more formal than "muzak", then the term you're probably looking for is Piped Music

Piped music is recorded music which is played in some supermarkets, restaurants, and other public places. (Collins English Dictionary)

Besides Muzak the term elevator music is common, too. Merriam-Webster has an entry for it. Their definition includes music played at retail stores ;-).

At least closely related is the term Ambient Music which has not been mentioned yet. Brian Eno popularized the term with his album Ambient 1: Music for Airports in 1978. The music was explicitly meant to serve as an acoustic background in public spaces.

Lawrence already mentioned the band Porcupine Tree and their song "The Sound of Muzak". In its lyrics this type of background music is referred to as "Elevator Prozac".

Hear the sound of music
Drifting in the aisles
Elevator Prozac
Stretching on for miles

Could this be the 'P' you're thinking of?

It is music specifically designed for shopping. Shopping Music. Tom Waits calls it out as good music for romantic conversation in the intro to "Better off without a wife" on "Nighthawks at the diner".

Put a little nice music on, maybe you put on some shopping music, something that's not too interruptive. Then you slide over real nice...

Now granted he's talking about taking himself out on a date, but calling it shopping music evokes the proper emotion in anyone who has ever experienced it.