Achim Blumensath writes:
 > > for the theoremstyle template type a good name could then be something
 > > like \EndThisTheorem.
 > I think it would be a good idea to uniformly call those commands
 > \EndThisEnvironment.

the problem with this and perhaps the problem with the whole mechanism is that
a lot of people have learned to write environments like this:

\newenvironment{foo}{...\quote ...}{ ... \endquote ...}

ie without using \begin/\end internally.

if all such things like \quote internally use \EndThisEnviornment then guess
what happens. so this needs some thoughts.

 a) do not allow above usage
 b) do implement your independent stack handling for these things
 c) do provide your own groups already at the environment-template level
 d) ...?