Way back, a couple decades ago, when I first started playing D&D, we had no named gods. Clerics were holy warriors, and the whole gods thing was ignored.
Then I saw the Greyhawk gods being statted and described in Dragon magazine. I and a couple of my Players liked these gods, so they became the (default) gods for my homebrew campaign.
Later, when I was doing more indepth work on my homebrew, I discarded the Greyhawk gods, and created a long list of my own gods.
Occasionally we split play between my homebrew world and the World of Greyhawk (1983 box). When in my world, my gods. When in WoG, GH gods.
When starting my latest campaign world, I played around with creating new gods. I had several neat ideas for a pantheon, but I also wanted to keep things simple for bringing in a whole new group of Players.
At that time, I was regularly reading a story hour about a campaign that took place in a homebrew world. But the gods were the Greyhawk/generic gods from the PHB. It occured to me how easily the GH gods as listed in the PHB worked into any standard D&D campaign. Everyone playing the game and reading the story hour knew Farlanghn and Pelor and Hextor as easily as they knew clerics and fighters and monks.
The concept of a paladin of Heironious is now as natural to comprehend as an evoker wizard. The names of Nerull and Obad Hai are as generic for D&D as the names Mordenkainen and Bigby. The GH/generic gods were a fine match for a standard D&D campaign.
So, I decided to just accept the PHB gods into my new campaign. I have now fully integrated the PHB gods into my campaign world as if I had created them myself. They fit just fine, and the gods are one less thing new Players to my campaign have to read up on to enter play.
And most players I have met recently don't know anything about Greyhawk anyway, so they have no concept of these gods outside the PHB.
Quasqueton