I'm not sure I understand your logic. "class plgGroupPluginname
extends JPlugin" is how every plugin I've seen in Joomla works, if you
name your plugin "plg_GroupPluginname" you will likely encounter
problems. The logical extension is that this is already the name
defined for plugins, it's already unique and it's in the style.
Perhaps we could have done a better job of naming things when they
were introduced but that time is a good half a decade ago. Components
are similarly named "com_componentname" and modules are named
"mod_modulename" so these are used for them as these are prefixed
names used for these extension types. So the rule is to take what it
is the existing unique name and append the value. For plugins this is
different because plugins are actually a composite of two unique
values plus "plg" as a prefix instead of "plg_". An unfortunate side
effect of being established for a while is legacy decision which with
hindsight turn out to be bad.
The installer adapter for modules should be passing lower case so
that's a bug somewhere that should be fixed.