I saw the movie again today and was watching out for the shuttles.
The shuttle that McCoy and Marcus used to land on the 'planetoid' was number 4 I think. I looked for a named and didn't see it. Just Enterprise and a big number.
I'll confirm that it was a number 7 shuttle that tipped over on the flight deck and maybe a number 2. They're not writing their names in big letters like they did in the good 'ol days so I couldn't read the name either and it was very fast