There were probably a lot, but I remember "Call/370", which I think was
one of the first commercial ones.
==
I have an Auerbach report on timesharing services which I'll try to dig
up, which gives short company histories for many of the early commercial
services. Most of the major computer companies were offering some service
by the late 60's. Part of IBM's antitrust settlement with CDC was that
CDC got IBM's service bureau operation. GE timsharing stuck around for
a while. Tymeshare was one of the earliest independents, bootstrapping
themselves and fixing tons of bugs in the GENIE code.
I also forgot to mention HPs timeshared basic and 3000 systems, also from
the very early 70s ( the 3000 being HP's 'real' timesharing machine, so
they said)