Oh, boy: contranyms! Can't wait to see the other four Anu comes up with.
By the way--is -nym related to name?

One and the same. PIE root nŏ-men.

BTW, I wish people would lay off that cleave/cleave thing. Two different words that just happen to be spelled and pronounced the same.

By the way--is -nym related to name?

Yes, Greek ονομα (onoma) 'name' is related to English name and Latin nomen. The -y- crept in from another Greek dialect. It was originally pronounced like an u. Variations between o and u are rather common in many different IE languages.

cleave

What about to, two, and too? Three different words all spelled differently but pronounced the same. Unfortunately, their meanings are not opposites.

[Edited to correct typo.]

last week I posted this:
the worthless word for the day is: smug

[perhaps back-formation fr. smuggling]
to steal, filch, run away with

"What did that mean about the smugging in the square?
Why did the five fellows out of the higher line run
away for that? It was a joke, he thought."
- James Joyce, A Portrait of the Artist.. (1916)

which elicited the following smug response:

It means to show excessive pride in oneself. This is obsolete.

Sent from my iPad

No one ever thinks them the same words like cleave and cleave. I just think that it's way more interesting when a single word diverges in meaning so much that it ends up with antonymic meanings. There's even single-ended words, like black, that started out one way and ended up totally opposite.

"Enjoin" is not a contranym. One either "enjoins to" or "enjoins from". Either way, "enjoin" simply means "instruct sternly".

My favorite contranym is the phrase "cleave fast". The verb and the adverb reverse as a team to say that the subject goes to one extreme or the other.