* Βασίλης (Vasilis): This is the most common and widely accepted spelling in modern Greek. It's a very popular name.
* Βασίλειος (Vasileios): This is a more formal and traditional variant, the full form of the name.
Therefore, while Βασίλης (Vasilis) is the most practical and common answer, Βασίλειος (Vasileios) is also a correct rendering depending on context.