When a married man keeps a another unmarried women for sex, she is called a "keep" or "kept women," right? In the same way, a married women may keep an unmarried man to have sex with him. I want to know the exact name for that man.
The corresponding gender counterpart for a man in this relation is simply a "kept man". The terminology is parallel.
A man who is supported financially by a lover.
1917, David Graham Phillips, Susan Lenox: Her Fall and Rise, ch. 17:
The kept man—in and out of marriage—is quite a feature of life in our chaste little village.
1984 Nov. 19, Richard Zoglin, "Video: Small World," Time:
A strapping Italian hunk, he becomes the rich actress's kept man, uses her money to start himself in business.
The phrase 'kept woman' was more common in the past when most women were not financially independent; it implies that a wealthy man is supporting his mistress in a home he has provided for her, not just that he is having an extramarital affair. The reverse situation is less likely, but the lover of a wealthy woman could be described as a 'kept man', or, in modern parlance, a 'toy boy'.
The term "gigolo" can also refer to a kept man.
While it is mainly used to describe a heterosexual male prostitute,due to the industry differences between male and female prostitution, a male is often "kept" by one (or, a series) of women, with the understanding that he will probably keep other company to supplement his income.