In Swahili it’s kichwa farasi.
Thai uses “head” (hua, pronounced as two separate syllables, “hoo-a,” with that last A more of a schwa sound, NOT as “hwa” like in Chinese) the same way as English does, for a body’s head and a headland. A popular resort town down the peninsula a ways is Hua Hin (“Rocky Head”).
There may be a term for “nag” after all if we’re talking about horses: ma klaep. Pronounced “ma (high tone is important) glab,” with that last A the same A as in “flat” or “hat.” In that event, Nag’s Head would be Ma Klaep Hua. I’m not 100% certain ma klaeb is exactly right, though. And most people would just say “old horse” (ma kae).
On a somewhat related note, I used to live near the town of Horseheads, New York. I had noted the rather unusual name in the past before moving there. I had assumed it was named after some geological feature that resembled a horse’s head or maybe it was an English rendering of some Indian name.
But when I moved there I found a big sign in the middle of town explaining how they got the name. During the Revolutionary War, a detachment of soldiers ran out of supplies and had to eat their horses. The heads were considered inedible so they got left in a big pile. A few years later, settlers moved into the area and decided to name their settlement after the most distinguishing feature they noticed - a pile of decomposed horse heads. And while many colonial settlements changed their names over the years, this one stuck.
As I commented to friends in the area, at least they hadn’t decided to settle down on the site of the soldiers’ old latrine.
Backing up along the branch a little and going back to French, using a Québecois slang, a literal translation meaning “head of the old horse” (with broken down implied) could be “tête de picouille”
One of my elementary school teachers used to tell us to hurry up with “grouille ta picouille!”
I wasn’t totally clear on what, exactly, a “head” is, but apparently head = cape = peninsula. So my Bulgarian translation is “Полуостровът на Кон” (“poluostrovut na kon”). A literal translation would be “Главата на Кон” (“glavata na kon”). I’m not sure that that really means anything.
Nag as in “naggy woman” could also be bruja (lit. evil witch), pécora (lit. sheep but I’ve never heard it used to mean sheep), mala pécora (more emphatic).
Head as in cape can also be punta (think Punta Cana), lengua (this would be more for a cape that widens into a small peninsula). If the istmo sometimes gets overflooded, the place can be called an isla or ínsula (island), even if the overflooding happens only a few times a year.
In Catalan, I don’t know a specific word for nag as in old horse, but an online dictionary from the Catalan Government gives rossí (a similar Spanish word, rocín, means horse but doesn’t imply “broken”). Cap d’el Cavall Vell would mean Old Horse’s Cape; Cap de la Vella Euga, Old Mare’s Cape. Cap de la Vella, Old Woman’s Cape. Punta de la Vella Bruixa, Old Naggy Woman’s Cape.
In Hebrew, perhaps “Kef Hasusa”.
Or possibly “Rosh Nudnik”.
For the French, I’d prefer cap du canasson, which uses cap, which has the wordplay of the original, although the definition of “head of an organism” is archaic.
But, then again, I only took French as a kid, and took the singer’s version later. I’m not using any actual experience, just a dictionary, and verifying online.
Doesn’t that mean “fun of the horse”? 
Spelled differently. “Kef” with a Yod does indeed mean fun; “Kef” without a Yod is a variation on “Kaf”, or palm (of a hand), used to describe the geographic feature.
I’m pretty sure it’s a neologism, intentionally similar to the English word “cape”. Hebrew has a tendancy to adopt foreign words while giving the Hebrew meanings. For instance, the Hebrew word for “Cholera” is “Cholira”, from “Choli Ra”, or “bad illness”.
Ir: “rinn an chlibistín” (geographical feature); “ceann an chlibistín” (anatomical feature)
I couldn’t think of the Irish for nag, fair plé!
It’s not a word I knew; I found it in the dictionary. But having checked a couple of dictionaries it seems to be right.
Japanese： 「老い馬の頭」 Oi Uma no Atama
Kannada: [ಮುದಿ ಕುದುರೆಯ ತಲೆ] Mudi Kudureya Tale (You probably cant see these)
I can’t see the first one but can the second. The letters look vaguely similar to Thai, so it must be readable for my computer.