Can I use different company names and logos for different client interfaces?

Yes, you can create different template groups (Admin CP > Templates > Groups > New) and specify "Company Name" for each template group accordingly. For different logos, "header" template can be modified for each template group from:

 Admin CP > Templates > Templates > General.

Following code needs to be modified at the above mentioned template:

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<div id="topbanner"><a href="<{$_baseName}><{$_templateGroupPrefix}>"><img border="0" src="<{$_headerImageSC}>" alt="Kayako <{$_productTitle}> Logo" id="logo" /></a></div>

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Here, you need to replace src="<{$_headerImageSC}>" code with logo image URL.