Basic block functionality: How can I seperate the human and computer readable names in the block view?

Seems like the view you create just has one name.
I want to have two names, like 'view_1" for the view as a function and "First View" for the block to move around in the block view.

How do I accomplish that? Cause I still need to name the view as 'view_1' cause I use custom tpl.php files with the same name.

I've looked in Views and there I found 'title:' and 'name:' under basic settings.
Neihter of those changes the name of the view in the block view.

In the block view you can configure a block and override it's title.
I've done that but it still stays the same.

Is this a bug or what am I doing wrong?