I wonder if they ever tried to sue over use of the name ?
The Firm which did Star Trekking were formed in the early 80's releasing a few singles in 1982/1983. In 1987 they got a new record deal and put out Star Treking (UK no.1) and other singles upto 1992. They put out an album Serious Fun in 1987. They didn't split up or anything like that during the 80's. Obviously Page was unaware of them and whether the 2 bands knew of each other we may never know. But I think they'd hold more rights to The Firm name than Jimmy Page and Co.