Is there a name for a "moving meridian" corresponding to particular solar time?
This is better suited for English Language &amp;Usage SE, but the word you're looking for is 

Isochron


  an imaginary line or a line on a chart connecting points at which an event occurs simultaneously or which represents the same time or time difference


(Source: Merriam-Webster)

Isochrons are typically used in diagrams rather than maps, for techniques like rock dating, where correlating things by time is more important. 

But cartographers are used to putting all types of isarithms on maps, and would understand what an isochron was meant on a map.

The trick is to define "same time" as "same solar time", giving you the "moving meridian" you're looking for.

You could contrive a more specific term like isoheliochron but it hardly seems worth the effort, because they're pretty boring on a map.