The V-Strom requires more chain slack than most streetbikes. If you and/or the shop mistakenly set the chain slack as you would on any other street motorcycle, it's likely too tight and will bind while in use, causing the rapid wear. This could also bend the countershaft, so please look up the correct procedure and slack.
The rear wheel and axle components could have been reassembled improperly (leaving out or mixing up spacers is a common mistake), or the rear wheel could be misaligned. Tire monkey is lowest-paid, lowest-status position in the shop, so these sorts of mistakes are common.
Or, maybe the chain and sprockets are just worn out. You mentioned you bought the bike recently, and people who sell bikes are rarely motivated to replace chains and sprockets (or tires, for that matter) that are nearing the end of their service life. Chains also wear unevenly, so if chain slack was not set at the tightest point, it will bind as above.
A fourth possibility is that the previous owner installed low quality chain and/or sprockets -- eBay is full of cheap, dangerous low-rent chains and sprockets. Or perhaps they replaced the chain and not the sprockets, which would cause rapid wear.
Put the bike on the centerstand (if it has one) or on a rear stand and check it out thoroughly -- check the alignments, rotate the wheel and listen for problems with the bearings, see how much the sprocket carrier can move relative to the wheel, inspect the sprockets, look for tight spots in the chain, etc. and so on.
2002 Suzuki DL1000 V-Strom, Dark Metallic Space Blue
1983 Suzuki GS850G, Cosmic Blue
2005 KLR685, Aztec Red - Turd II.2, the ReReTurdening