This is my soulmate...

You say: Hi, this is my girlfriend Mary or Hi this is my boyfriend John. If you are not married but living together ,you would say: Hi, this is my partner Mary or Hi this is my partner John. If you are engaged, you would say: Hi, this is my fiancee Mary or Hi this is my fiance John.

This is my girlfriend/boyfriend/partner. "Partner" is the favored expression here.

they are lover

This is my girl friend................ This is my boy friend.........