No, the origin of the term neoconservative is the socialist, Michael Harrington. He used the terms as a derogation of “splitters” such as Irving Kristol and Norman Podhoretz. Kristol and Podhoretz began to use the term as an ironic honorific, then later used the term in a more neutral sense.
Interesting.
I didn’t realize that the label, “Neo-conservative” was a derisive term used by a student of the Trotskyite, Max Schactman to identify other former Trotskyites.