vCenter tasks and events will actually show you exactly that. The tasks performed by which user from which IP.
Additionally you can find established sessions with their username and originating IP in the vpxd-profiler.log files but they are a bit tricky to parse if you have never done that before.
Actual SOAP message logging is also possible by bumping up the vCenter log level (I am not entirely sure if trivia is needed or not on that).
A third option would be to utilize the free Log Insight option with the vSphere dashboard, see screenshot below.

Hope that helps.