Here we see the assimilated Captain Picard as Locutus
I am Locutus of Borgemphasis mine
Why do The Borg refer to themselves simply as Borg?
Linguistically challenged or just ultra cool?
The Borg are a single entity hence why its just Borg. Because they are a single entity you could think of their name like the name of a major corp, for example Wal-Mart. Lets now assume Locutus works for Wal-Mart.
I am Locutus of Wal-Mart
Sounds a little silly still but we can also think of Borg as being a nationality, or race. so say Locutus is from Russia.
I am Locutus of Russia
When Thinking about the Collective like this, it makes more sense in the way Picard says of Borg.
In both French and English, surnames also would have been something to this, Joan of Arc (notice of arc). OR for example Joan lived in Paris, Joan of Paris.
This is actually a very unusual event. The majority of Borg we see refer to themselves as "we". They also have designations, rather than names. The use of "I" is in fact a plot point in the later TNG episode "I, Borg".
Locutus was not a normal Borg drone, as we can see in the episode, and elaborated on further in First Contact. He was an emissary, and thus received a name/title (this isn't clear) and a slightly different connection to the collective. The Queen was originally trying to create a "consort" (at least according to memory alpha) of sorts, another semi-individual.
So Locutus' use of the phrase "I am Locutus of Borg" is him representing the collective. Compare "I am the ambassador of Bavaria" or "I am Lord of Camelot". Any grammatical oddity is with his name/title, which we are not told exactly what it represents.