After the filmmakers toyed with the "radical" notion of calling the ship the USS Iowa, the name Kelvin was chosen instead. According to writer Robert Orci, the starship was named for real life physicist Lord Kelvin but also just happens (*wink*) to share a name with JJ Abarms' grandfather, Harry Kelvin, whose birthdate, May 14, was used for the ship's new registry, NCC-0514.
In-universe, the USS Kelvin's name would live on in Star Trek Into Darkness' Kelvin Memorial Archive and in Star Trek Beyond's personal escape pods, Kelvin Pods.
In our universe, the name Kelvin shows up in just about every JJ Abrams produced television show or movie, including Kelvin Inman from LOST, Kelvin Genetics in Fringe, Kelvin Gasoline in Super 8, and Kelvin Ridge in Star Wars: The Force Awakens.
On an even larger scale, "Kelvin Timeline" has come to be the official moniker of Abrams' rebooted Star Trek universe – coined by Michael and Denise Okuda in their 2016 edition of the Star Trek Encyclopedia.