Yup. Or the client name. Or a combination of the two.
The most common structure starts with two folders:
"src" is where you put the code that you write specifically for this project. "vendor" is where you put third-party code and libraries.
Within "src", your folder structure would match your namespaces.
I think "core" might be too general of a name. It seems like you're putting base classes of all kinds in there. It would probably be better if BaseController lived in the Controller namespace, BaseMapper in the DataMapper namespace, and so forth.
It's most important that your folder names -- case and all -- match your class and namespace names -- case and all -- because file systems can be case sensitive. With that being said, the prevailing standard for class and namespace names is upper camel case, which means that, yes, your folder names would also be upper camel case.
Mostly it doesn't matter. Though, the PHP community seems to have settled on singular for namespace names (and thus also for folder names).
Using the new structure above, you should only need:
$classLoader = new SplClassLoader('ClientName\\\\ProjectName', '../src');