「独占欲」というなら
desire to keep someone to oneself (誰かを独占する願望)
のように言えますが、恋愛関係での独占欲は possessive を使ってよく言います。
例:
He's really possessive about his girlfriend, he needs to know where she is all the time.
「彼は彼女に対して本当に独占欲が強いんだ。彼女がいつもどこにいるか知っていないと気がすまない。」
She's very possessive towards her boyfriend, she doesn't like it when he spends time with any of his friends.
「彼女は彼氏に対する独占欲が強いから、彼がどの友達と出かけるのも気にくわない。」
このように
He's really possessive about his girlfriend
She's very possessive towards her boyfriend
のように言えます。
ご参考まで!