The name actually comes from the name of the proposed satellite
The name of the system first appeared early in April 1955 on an NRL
document entitled "Proposal for Minimum Trackable Satellite
NRL = Naval Research Laboratory
Final Report for the Minitrack Tracking Function Description
In early April 1955, Milton Rosen, John Mengel, ...
According to Wikipedia, they're all related: Project Vanguard launched Vanguard satellites on Vanguard rockets, but only 3 of 11 launches succeeded. The US Naval Research Lab that ran the project doesn't have much to say about it.
This picture (from the document linked below) shows the Vanguard engines; the first stage engine is in the rear.
The engine was an X-405 built by General Electric. The launch vehicle was built by Martin Marietta. These two contractors differed on the exact cause of the explosion, as the question states.
The Martin people traced what they ...