"Badeying" is a slang word commonly used to describe someone who is being overly dramatic or theatrical. There are several synonyms that can be used instead of "badeying," such as overacting, exaggerating, dramatizing, melodramatizing, or hamming it up. All of these terms describe a person who is drawing attention to themselves by acting in an exaggerated manner. However, depending on the context, some of these synonyms may be more appropriate than others. For example, dramatizing could describe a more serious portrayal of a situation, while hamming it up implies a humorous or comical performance. Regardless of the synonym used, it's clear that the person in question is seeking attention and trying to make an impression.