Considering that the car recommends Mobil 1 Synthetic oil as per the logo on the oil cap, how can I be sure the garage that did the oil change poured the recommended oil and not another low cost oil to save money?
My first suggestion would be to ask whoever did the change. If you are seriously in doubt, provide the oil to somebody to redo the change, or simply do it yourself. If you are able to do the change yourself, I would suggest learning to do so (just keep the receipts so you can provide them as maintenance records in the event you wish you sell the vehicle).
All in all, if you aren't certain the right oil was used the first time, redoing a $40 oil change with the correct oil will be way cheaper than any damage the wrong oil might inflict on your vehicle over time.
Other than draining a bit and sending it off for some analysis, you'd have to watch them do the oil change. Though if you are that concerned about trickery, your time is probably better spent asking around for references for a reputable shop.
The only way I know of at least here in Iceland is basically to ask the garage, although here the dealerships certify garages that use only the proper oil for each make
I would suggest taking a look at the quality of the oil filter.
The oil filter doesn't, strictly speaking, tell anything about the quality of the oil, but it does say something about the people/company who changed your oil. If they used a high-quality filter, then it's more likely that they used a high quality oil. Similarly, if they used a low-quality filter, it's more likely that they used a low-quality oil.
If you take out the filter and it looks like this:
or worse, looks like this:
then I really think it's safe to assume that they didn't use high-quality oil either.
Also, this is one of the reasons why I chose to do oil changes myself. You know which oil goes in, you know which oil filter goes in, and you know that you've properly replaced the O-ring and the crush washer, which many shops seem to forget.
No real way to tell from the oil itself (although Royal Purple IS purple).
Either ask the shop or change it yourself.