I did a quick bit of searching to find out what naming conventions were used. It turns out that there isn't really one.
C# appears to becoming very popular with Unity developers, if not the dominant language but as the syntax is similar most people can mix and match if needed.
As C# is a Microsoft language many people have adopted the Microsoft guidelines for the use of case when working in Unity. I also prefer those naming conventions for case, they are:
PascalCase for public and protected properties and fields and camelCase for private properties and fields with PascalCase for all methods independent of if they are private, public or static etc.
The case is only significant for public or protected elements so that non-case sensitive languages can always reliably access them:
Some people like to use an underscore in front of _camelCase for private fields but that is their personal preference and appears to go against the recommendations in some of Microsoft's guidelines. Again, that is only significant for public fields, what you use privately is just for readability of the code.