I found myself needing time to think on this one, and I'm glad I took it. After reading this, and all the replies thus far, I also will speak against the use of class in favor of an alternative (which I'll get to in a moment). The reasons:

1. I realize that the desire for a succinct name means toplevel is a given, but there is no need, IMHO, for using the all-lower version. Thus, Class would be preferable to class
2. But, the word 'Class' has very specific connotations. From a learning point of view, I don't think it is immediately obvious what "use Class" does, and I can see it being confused (by a newbie, for example) with just plain use, and I don't think it makes it sufficiently clear that we using a module named "Class" to do the work.
3. What you're really doing is offering the opportunity to use a shorter class name, not use a class in general, as "Class" or "class" would imply.

Considering these things, I think any form of class would be out. What would I suggest? How about Shorter? I think it reads well:

use Shorter 'My::Company::Namespace::Customer';
use Shorter 'My::Company::Namespace::Preferred::Customer', as => 'Pref
+erred';
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