Yes. Once you are crowned Miss Universe, you serve as such for the following year, and you are forever known as "Miss Universe xxxx (insert year)." The only exception is if you resign or are dethroned.
That is Sushmita Sen. She was born in Hyderabad, Andhra Pradesh, India, on November 19, 1975. She was crowned Miss Universe in 1994. There was one other Miss Universe from India, and that's Lara Dutta. She was crowned Miss Universe in 2000.