In astronomy Is there a name for the exact time between solar noon and sunset?
No, there is no such word better than "afternoon". I can't think of a situation that would require technical language for this period of time, the exact point halfway. When astronomers want to be technical about time they use UTC or UT1 or AT1 or any of the other "times". When they want to talk about more loosely defined periods they use "morning", "afternoon", "evening" just like everybody else.

"Mid-afternoon" is an ill-defined period, from about 2pm to about 4pm