Ancient Romans had no special sleepwear. They typically slept in their underclothes, which they also would have worn around the home. Here's a relevant quote from Everyday Life in Ancient Rome by Lionel Casson. The morning toilette for the master of the house was simple and quick. As was the universal ancient practice, he had slept in his underclothes—a light sleeveless knee-length tunic and under it a loincloth, which functioned as undershorts. It took him but a moment to slip on his sandals... and if his day included a formal morning call or a session in the Senate or law courts or the like, put on his toga.