For my Re-imagined Constitution Class to finish this project I worked out the maximum amount of shuttles is 8 if the Captain wishes to have a full complement, unless he or she might decide on less.
I used the names of those scientists I find interesting for the other shuttles not otherwise having appeared or mentioned in Star Trek.

Name / Episode or Source
Aristarchus / Aristarchus of Samos
Columbus * / The Galileo Seven
Copernicus * / (Star Trek V: The Final Frontier)
Kepler / Johannes Kepler
Huygens / Christiaan Huygens
Einstein * / Metamorphosis (updated VFX)
Galileo * / The Galileo Seven
Sagan / Carl Sagan

Using this older WIP of the hangar and cargo area to help illustrate, 2 Shuttles could be parked for use in the landing bay launch receiving area, in the deck below reached by the turntable / elevator there is room for 4 shuttles to be stored, then on the lower deck, the main cargo area there is space for 2 more shuttles adding to 8 shuttles.

This could be down to what the Captain wants, might decided on having 4 or 6 is more cargo space is what is needed.