Some riders probably can't even remember the last time the gear case lube was changed while others do it every engine oil change. For the record, a complete change is recommended every 24,000 miles (check the level every other oil change).
Choice of gear lube is up to you. If you use synthetics in your engine/transmission then maybe you'll want to do the same with the gear case. If dino has been your preference then by all means stick with it. Just follow your manuals recommendation for weight. What's 'really' important is how you fill the case.
If you have a Nomad this will be simpler if you remove the left saddlebag. If you have aftermarket pipes on a Nomad you 'might' have to loosen or remove the left side muffler or raise the bike on a lift so the swingarm drops to get the drain bolt out.
Remove both the drain bolt and the fill cap and let the old lube drain into a small container. There isn't much (200 ml).
Once drained, put the drain bolt back in the gear case and, if you have a torque wrench calibrated in inch pounds crank it down to 78 inch pounds otherwise just snug it down with a 1/4" drive socket or short box wrench.
To refill the case the factory service manual says to bring the bike up so it's level or as close as you can get without it falling over. The neat thing about Nomads is you can put a jackstand or other prop under the right side engine protector bar and block of wood under the kickstand and your bike will just sit there all day perfectly level. See 'Level It' Here.
Now that I've provided the 'official' method let me provide a recommended alternative. Sometimes with machines, owners discover what the factory recommends may not always be the best way to do things and after many years and probably millions of miles of combined experience Vulcan owners have discovered leaving the bike on the sidestand when filling the gearcase seems to result in fewer leaks down the road (no pun intended). So, skip all the leveling (unless you'll be checking engine oil level) and just fill the gearcase with the bike on the stand. The difference in the amount of lube added is very small, there's no danger of damaging the internal parts and for reasons unknown there seems to be less chance of a leak developing in the future.
Fill the case through the large opening until the case starts to overflow or the oil level reaches the threads on the opening. DO NOT OVERFILL. Let the assembly sit a moment until you're sure it's full but no extra lubricant will drip out the fill hole then put in the plug. Clean it all up and you're finished.