Given that it first makes an appearance on the US list in 1969, the name's sudden surge into popularity is almost certainly in part thanks to popular daytime gothic soap Dark Shadows introducing the character Jamison Collins that year. In fact, one actor from the show (David Selby) did indeed specifically name his son - born 1969 - after the character.
Jamison "Jamie" Reagan is a character on Blue Bloods. He is the youngest out of the siblings. After graduating from Harvard Law... he gave up a promising career in law to follow in the family footsteps as a cop.