What would male concubines be called?

I've always heard a phrase used for this: male concubine. (It is, in fact, such a natural term for this that it's used in the question itself.)

Here are some examples:

The rise and fall of Emperor Qian's male concubine — South China Morning Post

Women were forbidden from taking a male concubine. — Wikipedia: Islamic views on concubinage

You may also be able to borrow a term from another culture, if that's what's being discussed. For example, when discussing the Romans:

[M]any well-off Roman men kept a male concubine called concubinus — The Evolution of Same-Sex Attraction

Finally, when talking about a modern-day relationship, there are more words available. (But the word concubine wouldn't be used here, not for a woman or man.) The term that comes to my mind is side-piece, which although being most commonly applied to "the other woman" can also be used for a man:

A side piece in an affair is not gender specific. Hollywood has portrayed the side piece to be a woman or a victim of the "situationship", imposing double standards. Typically, cheating is associated with men, and the language used to describe it include jump off, side piece, and mistress, which refer to men sleeping with multiple women. Yet we don’t talk about women doing the cheating, or women having a man as their side piece. — Medical Daily

If it's a monarch or other important person - I don't think regular people get to have concubines - "Favourite" is often used. James I had "favourites" who were always attractive young men, and Potemkin is often described as Catherine the Great's most famous "favourite".

https://en.wikipedia.org/wiki/Favourite

Concubine is interchangeable. Given the -one suffix would denote a male and concubone is not a word, concubine serves for both sexes.

Lexico sheds some light as to the etymology of 'concubine':

Middle English: from Old French, from Latin concubina, from con- ‘with’ + cubare ‘to lie’.

The nominative singular noun, concubina, with the suffix -a, implies a feminine form (see also here), and the male equivalent would be concubinus (also 'bridegroom'), which is corroborated by Etymonline.

The fact we only have a single word is arguably more of a testimony to our hetero-normative and androcentric history than to the origin of the word.

A short but more nuanced article on the usage of both terms can be found here.