If you're inconsistent with lexical variables like my($fooBar, $quux_xyzzy), then that's fine by me. It may slightly confuse people hoping to delve into your code, but that's probably only a small number of people.

However, for public functions/methods - for the API you expect other people to code to - you should aim for consistency throughout a module or collection of related modules.

Generally speaking under_scores seem to be the most popular way of naming functions and methods, so unless you've got a specific reason to use another naming convention, should be the default option. Good reasons to use camelCase or runtogetherwords might be:

• consistency with a specification - for example, an HTTP library might name functions or methods after HTTP methods which are conventionally written in uppercase, so it migh make sense to name methods like $object->POST and $object->GET.
• porting code from another language - if you've ported a library from another language, then it makes sense to keep the original case of function/method names. This allows your users to easily understand the documentation and examples of the source library and apply that knowledge when using your port.
• inspiration from another language - perhaps your code is not a direct port of a library from another language, but aims to be a work-alike.

I saw it just the other day in Web::Magic 0.005, didn't bother me one iota. I have to lookup the documentation either way. Web::Magic