Why a-variable-name ia not a valid variable name?

Answer 1

Because it has the '-' character. A valid name would be a_variable_name.

Answer 2

Depends upon the programming language. For some it's valid, for some others it isn't. If I were to guess as to why, I'd say it's because '-' is also an operator symbol, but I'm merely speculating.

https://en.wikipedia.org/wiki/Naming_convention_(programming)