The voice for Grey was performed by Majel Barrett.
Their name originated from a scripted source.
The novel Forgotten History, expands on this, explaining that "Jan" is short for "Meijan." The novel depicts her as serving as the inaugural Director of the Department of Temporal Investigations from 2272 to 2275. She is actually responsible for Spock's erasure from history, due to her scanning the time of his rescue while he was not there. Feeling guilt over the role she played in his death, these events add to her concerns about interfering with time.