Honestly, even when my TV mount can reach two studs, I still attach a 2"x3" to the studs, then attach the mount to the 2"x3". Reasons:
Studs aren’t always going to be centered on the mount. Yes I know some are meant to handle this, but it seems less than ideal.
The 1.5" or so gap you get between the mount and the wall because of the 2"x3" is useful for cable management.
Seems way stronger (haven’t tested but it just feels that way)
if you need to move the TV left and right, you’re just putting more holes in the 2x3, not the wall (yes I know some mounting brackets allow for a level of left-right adjustment, but not all of them do)
You’ll need 2-2x3 (or 2x4… but 2x3 is cheaper and plenty strong enough) that is long enough to span between 2 or more studs. 1 is for the top of the mount. 1 is for the bottom of the mount. Attach them to the studs so they are level and parallel and the spacing between the 2x3s is the same as the spacing between the spots on the TV mount that where the bolts/screws go through.
Note: you have to use structural wood screws or lag screws that are of sufficient length to go through the 2x3, through the drywall, and attach sufficiently to the stud in the wall. You’ll likely want 3.5"-4" structural wood screws or lag screws. It won’t hurt to also use flat washers so the structural wood screws/lag bolts hold even better and don’t pull themselves through into the 2x3.
Good luck! Have mounted several TVs for myself and others (up to 92" screens) and haven’t had one fall off yet!