I've always liked the name Peri. In mythology, a Peri is a creature that's part angel and part devil. Reminds me of some of my old girl friends.
Peri comes on board the TARDIS in the "Planet of Fire" story. The other two companions, Turlough and Kamelion, leave in this story so Peri is left as the only companion. In the next story, "The Caves of Androzani" the doctor gets himself killed and regenerates. Never a dull moment on the TARDIS, Peri probably thinks he does that all the time.
Peri stays on board until "Mindwarp", the second part of "Trial of a Time Lord. where she ends up marrying the King of the planet Thoros Beta. Well, not exactly. "The Mysterious Planet" is a flashback to a previous adventure of Peri and the Doctor that the Gallifreyian court wants to use to convict the Doctor of meddling with the laws of time. So Peri has already left the Doctor in the past but Nicola Bryant still has to show up for work every day to show the flashback to the Gallifreyan judges. Gallifreyan trials get a bit complicated.
Peri is played by Nicola Bryant (born October 11, 1964 in Surrey, England). Before her Dr Who gig, Nicola's acting experience consisted of er...nothing. The Who-Nerds accused the BBC of casting Nicola just because she was a beautiful young girl with big gotchabahootchies who favored low-cut tops. Yeah, you just can't put anything over on those Who-Nerds.
After Doctor Who, Bryant's career took a definite turn for the better. She did some extensive theater work and picked up parts on a lot of BBC TV shows including one I remember, "Blackadder's Christmas Carol."