Is Saint Nicholas really a saint?

Yes, there are several saints named Nicholas and the best known is Saint Nicholas of Myra
Saint Nicholas (270 -346) is the common name for Nicholas of Myra, a saint and Bishop of Myra (in Lycia, part of modern-day Turkey). Because of the many miracles attributed to his intercession, he is also known as Nicholas the Wonderworker. He had a reputation for secret gift-giving, such as putting coins in the shoes of those who left them out for him, and is now commonly identified with Santa Claus. The tradition of Saint Nicholas Day, usually on 6 December, is a festival for children in many countries in Europe related to surviving legends of the saint, and particularly his reputation as a bringer of gifts