When he turned to the Dark Side he forsook his birth name and took the name Kylo Ren. "Ren" is similar to "Darth" in that it is sort of a title signifying Kylo's membership in the "Knights of Ren", a group of other Dark Side followers.
We learned in an interview with Abrams in Entertainment Weekly, "Ren" is the title, which refers to a mysterious organization called The Knights of Ren. "Kylo" is the unique signifier, a name Kylo Ren chose for himself for some equally mysterious reason.
- cinema blend
It seems the meaning behind "Kylo" might be intentionally kept a mystery.
Is appears to be purely coincidental that his birth name and Ren are so similar as we have no further info on the subject of how the name "Kylo" was chosen.
Even more interesting, though also likely coincidental:
Ky + Lo = "Kylo", who is the son of a Skywalker and a Solo. The "ky" comes from Skywalker, and the "lo" comes from Solo.
It's just a possible out-of-universe connection, as in maybe the filmmakers came up with Kylo's name that way.