Well, when she was born she was called Agnes Gonxha Bojaxhiuas but when she joined the sisters of Loretta and took her vows she took the name of saint Thérése and changed it a bit because 1 of the sisters already was called thérése
hence: Teresa
Mother Teresa's name was changed from her birth name of
Agnes Gonxha Bojaxhiu to Sister Teresa when she became a novice in the convent in Ireland, at the age of 18. Sister Teresa's name was changed to Mother Teresa when she became a fully professed Sister. Later, when she started the Missionaries of Charity, she was still called Mother, as she was the Mother Superior, and Foundress of that Order.
Mother Teresa's original name was Agnes. On May 24, 1931, she changed her name to Teresa. It is unknown when she obtained the name "mother Teresa." The orphans that she took care of started calling her that, and eventually the nuns working with her did too.T.SHCL