Not wanting to share a loved one

What is a word for someone who does not like to share their loved ones?

For example if a guy doesn’t like his girlfriend to be around a guy that he know has a crush on her. He’s not jealous because that would mean he does not trust her, but he does trust her, but just does not want the other guy being around her. What is a word that describes someone that does not want to share someone they love with other people?

Jealous would indeed fit, even if he trusts her.

Possessive could fit.

Proprietorial is also very fitting. Defined as: behaving as if one owned a particular thing or person; possessive.

Depending on the intensity of the emotion, the person may simply be wary.

Jealousy has many meanings, and many people often disagree with each others' meanings. The word has existed in the English lexicon since the 13th century, and many notable writers and grammarians have had a lot to say about the word -- often comparing the word to the similar experience of "envy."

Many, including psychologists, often identify jealousy as the emotional reaction to the fear of someone taking or ruining something that you possess, which includes "distrust, anxiety, and anger."

More from Meriam Webster: Jealousy means unpleasant suspicion, or apprehension of rivalship. —Theodore M. Bernstein, The Careful Writer, 1965

There are three different ways in which jealous can be used. The most common is ... where the meaning is “fearful of losing attention.” Another broad sense is “possessive” or “protective” ... third usage is in the sense of “envious,” as of another person because of his or her belongings, abilities, or achievements. —William and Mary Morris, Harper Dictionary of Contemporary Usage (2nd ed.), 1985

Jealousy is properly restricted to contexts involving emotional rivalry; envy is used more broadly of resentful contemplation of a more fortunate person. —Bryan A. Garner, Garner’s Modern American Usage (3rd ed.), 2009