The latest issue of the Weekly Worker has a footnote drawing attention to the fact that documents about the debate within the Militant Tendency (then calling itself Militant Labour) in 1996 about changing its name to "Socialist Party" have been published on the internet here:
http://www.marxist.net/namechange/mainframe.htm
I have not had the time (nor, to be honest, the inclination) to plough through the pages and pages of turgid Trotskyist reasoning about the difference between a "united front" and a "workers party", but I did note that one of the reasons their leaders put forward for the change was it would help when they contested elections. Tough luck. They failed on that one.
Anyway, that's where the material is for anyone interested in going through it. Though they must have been aware of our existence and that we did use the name "the Socialist Party" nobody seemed to have raised this in the debate but I could have missed it if anybody wants to check.