In astronomy Is there a name for the exact time between solar noon and sunset? Like there are names for various events such as sunset, sunrise, solar noon, solar midnight, astro, nautical and civil twilight, what exactly is name for time between sunset and solar noon. Afternoon it is but what exactly between these two points? Is golden hour the only subcategory for the afternoon? 

I did come across the word midafternoon. similarly, midnight, midmorning and midevening. but then again midafternoon would mean 3 o clock or does it mean point between solar noon and sunset? because midnight in general is more acceptable as 12 o clock. is it?
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