You don't get Natalie, he/she means you will find sentences that starts with jina lakho nani, jina langu ni, jina lakhe ni. Your name, my name and his or her name.
Duolingo does not like contractions because in some language lessons it does not distinguish between is and has so you should avoid using them. Spell out is.
Nobody uses "my name's" to mean "my name has" in modern English except when has is auxiliary. It's just a matter of some contributor adding "name's" instead of "name is" in to a list of possible translations.
I am afraid you are mistaken. Jina means name. Lake means his or hers. Langu means mine. Lako means yours.
Jina just means name. It's my car = Ni gari langu. It's his/her car = Ni gari lake