I guess you have two options:
a) You name stuff so you know whats what (e.g. "Fancy Program (computer a)" etc)
b) You rename the "log" folder manually depending on which computer you are using
I would probably prefer solution a myself, but solution b could be semi-automated by creating for instance a few batch-scripts (say a computerA.bat which renames "logsA" to "logs", launches ZU and waits for it to finish, then rename "logs" back to "logs"; a computerB.bat which is similar etc)