Is NMDA produced in the body?
(my comment reiterating the answer seemed useful, so I've reproduced it here)

There are "NMDA receptors" in our body. There is not NMDA naturally in our body*. "NMDA receptor" is just a name people gave to one of the receptors that normally binds glutamate. They could have called it something else, like the "slow glu receptor", or "Glutamate Receptor A", but they called it the NMDA receptor because they discovered it was different from other glutamate receptors in that it was activated by a chemical called NMDA in their experiments. 



(original answer)

NMDA receptors are in fact glutamate receptors natively: there is no endogenous NMDA*. They are named NMDA receptors because experimentally they were differentiated from other glutamate receptors using the compound NMDA. At first glutamate receptors were known as "NMDA" and "non-NMDA" glutamate receptors, and later the non-NMDA sort were found to be sensitive to AMPA or kainate and named thusly.

Many other receptors are named this way: the nicotinic acetylcholine receptor is the receptor that nicotine is an agonist at, but the endogenous ligand is acetylcholine; muscarine is an agonist to the muscarinic acetylcholine receptor but the endogenous ligand is acetylcholine.



Watkins, J. C., &amp; Jane, D. E. (2006). The glutamate story. British journal of pharmacology, 147(S1), S100-S108.



*In the comments, @gilleain pointed out some research suggesting that NMDA does exist endogenously, although in fairly specific areas and not disputing that glutamate is the primary endogenous agonist for NMDA receptors. This work was long after the NMDA-sensitive glutamate receptor was discovered and named, but is some interesting trivia nonetheless.