This way if you do get a web certificate SSL that is valid on all sub-domains, www. is a subdomain and clientarea would be a subdomain. That's if you are going to SSL the entire thing.
The name of the folder in which WHMCS doesn't matter but rather than naming WHMCS you could name it /support/ or likewise create a subdomain support. so your WHMCS would still reside in the /support/ folder. Some suggestions for subdomains are:
You can use nearly any term that you like just make sure it's not going to be a term that's also going to be a URL in your Joomla SEF.
I'm not sure what your root SSL is or what it covers but you don't need a root SSL, just an SSL on your whmcs subdomain/installation.
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