The process of copyrighting the flash cards is actually not that difficult and you can do it yourself. The US Copyright Office has made it very easy to file for copyrights online on their website. You need to have a pdf (front and back) of the flash cards...though you can do it in one document that illustrates all of the work. You have to register with the US Copyright Office with a user name. You can then go through the filing process, provide your background information (name, address, etc.), upload the file and then make your payment (which is approximately $30). The whole deal will take no more than 45 minutes...start to finish.
If you are commissioning someone to create the flash cards, you need to have an engagement contract wherein you specifically state that any and all intellectual property that is developed as a part of the commissioning of this project shall revert back to you (or our company). You can have the other terms of a standard form personal service contract and you are then protected.
Technically speaking, to register the name, you can go one of two routes. You can trademark the name (which is also something that you can do without attorney assistance online at the US Trademark Office website for $300). You can also copyright the name via the same process described above.
I suggest that you first copyright the name...you can then affix the registered insignia. If this is something that you start to sell and market, at that point you can file for trademark protection. The US Trademark Office prefers to have a mark in use in commerce before granting an application.
One other thing relative to the name...be sure to run copyright and trademark searches on the name on the respective websites to make sure that it is not already taken by someone else. This will prevent an infringement claim but is will also make sure you are not spinning your wheels on a name that is already taken as well.
Let me know if you have any other questions. Please also rate my answer positively (4 or 5 stars).
BTW, I am a licensed IP attorney with over a dozen years of experience handling matters just like this one.