I cannot find a term for a truly unqualified time. When not given, a time system is still implied, and generally it will be “my time” (the local time for the person making the utterance), unless a different system is clear in context.
More formal terms are “local time”, “civil time”, and “local standard time”. Technically, these could be different. Local time is whatever the local population thinks of as the time, civil time is the time established by local civil authorities, and standard time is the time established by standards bodies that civil authorities might or might not recognize. But since the development of reliable clocks and the need in commerce for time standards, these are frequently the same.
It’s also possible for “noon” to refer to local solar time.
With regard to utterances preserved from the past, any unqualified time might have meant local solar time, mean solar time, or railway time, depending on the locale and the context.
For more information on these terms, see the Wikipedia article “Time Zone”.
“Wall clock time” is generally used to clarify that the time given refers to time of day, instead of some kind of elapsed time or cycle time. For example, you might say that a process ended at 10:20 (elapsed time), but at 8:10 A.M. (wall clock time).