Does Pepper Potts know that Peter Parker is Spider-Man?

In the MCU movies, yes. In current comic continuity, no. Pepper did know in the comics during Civil War (forget that stupid movie, it was a comic event) when Peter revealed himself to the world. read more

Clearly Tony made no effort to hide the suit and Peter's connection to it when Pepper walked out to announce the press was there, but even if that was the first time she saw Peter she definitely knew before. read more

If Pepper does make an appearance in the Spider-Man movie, fans will be glad to see her. When the first trailer for the movie debuted, audiences were quick to spot an easter egg which nodded to the character. Peter Parker was seen walking with Tony Stark in the Avengers headquarters, and the shirt he was wearing was one Pepper donned in Iron Man 3. read more

As Spider-Man declined the invitation and left, Potts asked Stark what they should do with the reporters. Stark asked Happy Hogan for a ring and planned to propose publicly, although Potts told him that she could improvise something better than that. read more