My garage has an existing receptacle for NEMA 10-50 which has hot-hot-neutral. I plan to install a NEMA 6-50 which requires hot-hot-ground. Can I just use the existing neutral wire as ground at the outlet side AND change neutral in breaker panel to connect to ground bus bar?
Not quite. You also need to destroy all the insulation on the neutral-to-be-ground wire which is accessible.
That's a subtle distinction in Code. You can't convert a hot to a neutral because the wire must be white its entire length. However, you can convert a hot or neutral to ground, because Code only requires you strip the insulation which is accessible.
However, don't do that. Convert to NEMA 14.
NEMA 14 is the "Universal solvent" receptacle that will power whatever went in that 10-50 (hot-hot-neutral) and also anything that takes a 6-50 (hot-hot-ground).
I presume your neutral wire has white insulation because if it was already bare, you wouldn't need to ask about making it a ground. I am saying leave it neutral, and add a ground.
Grounds, unlike any other wire, can be retrofitted. They can follow a different path back to the panel, they only need to reach anywhere that has a 10 AWG or larger ground path back to the panel, or even a conduit pipe. Or even the grounding electrode system, those copper wires going out to ground rods or water pipes. (You can't use water pipes, though).