With standard LaTeX you are able to check for the class in use
invoking the kernel command \@ifclassloaded. However, doing so
you cannot get the explicit class name, unless you want to loop
over every possible class name until \@ifclassloaded returns
true -- don't do that! With the help of the present package you
can obtain the name of the current class with significantly
less effort. Just load the package as usual:
\usepackage{fetchcls}; then, the control sequence \classname
will hold the name you were looking for.