Feeling groggy after a nap means you are named, at several removes, for a British admiral's coat.
The standard account runs like this. Edward Vernon (1684 to 1757) commanded Royal Navy ships in the West Indies. Sailors were issued rum daily, and drinking it neat caused serious drunkenness. In August 1740 Vernon ordered that each half-pint be mixed with a quart of water, served twice a day.
Vernon wore a cloak of grogram, a coarse stiff fabric, and sailors called him "Old Grog." The watered rum took his nickname. That is the story Etymonline repeats, with the word "supposedly" attached. Word Histories says the cloak tale has "all the appearances of a folk etymology," yet no use of grog before Vernon's 1740 order has been found. The earliest it cites is from 1748.
What is firm is the timeline. Etymonline dates grog to 1749 as a drink of spirits diluted with water. Vernon's order is dated 21 August 1740, although the surviving copy at the Public Record Office is unsigned and undated. Grogram itself is older. Etymonline dates it to the 1560s, from French gros grain, "coarse texture."
Groggy followed. It was first recorded in 1770 for someone who was "drunk, overcome with grog so as to stagger or stumble." By 1832 the word had left the bar and entered the boxing ring, where it described a fighter who was shaky and tottering on his feet. That is the sense we use today for a person who is dazed after poor sleep or a long flight. Horses got the word too: it was applied to hobbled horses from 1828.
Vernon left another mark. George Washington's older half-brother Lawrence served under him in the Caribbean. Lawrence renamed the family's Virginia plantation Mount Vernon in the admiral's honor, after he received it in the early 1740s.