Technically a woman doesn't choose to become a nun, God calls certain people to the religious life (that is where we get the word "vocation" from the Latin "to call"), and then they choose whether to follow God's inspiration or not.
She took her first religious vows as a Sister of Loreto on May 24, 1931.
Mother Teresa's family was devoutly Catholic and Mother Teresa was quite a religious girl even at a very young age.
Mother Teresa was a religious sister and sister do not marry.
Mother Teresa did not decide to become a Catholic. She was born a Catholic.
Mother Teresa spent her life doing charitable and religious work in India.
Mother Teresa was baptized as a Catholic the day after her birth.
It is traditional for religious to take a new name when they join a religious order. In the Sisters of Loreto, when a woman makes her final vows, she take the title of Mother. Mother Teresa took the name Teresa in honor of St. Therese of Lisieux, a patron saint of missionaries.
Mother Teresa was never married. She was a religious sister - a bride of Christ.
She was head of the religious order that she had founded: The Missionaries of Charity.
Mother Teresa was born and raised Catholic.
The choice of one's religious sect is mainly a factor of the family the person is born into. For example a child born into a Muslim family will likely become a Muslim. So like wise the story of Mother Teresa.
Mother Teresa has not yet been canonized as a saint and has only been beatified.