Siniy,
I presume it is not good enough to have in the template tiddler
text <<currentTiddler>>, [[mytemplate]]?
Since you know the name of the template when you transclude it, why not make a macro that creates a variable and transcludes the template?
Perhaps you could have a global macro of this form (tested)
\define displaytemplate(templatename)
<$set name=template value=$templatename$>
{{||$templatename$}}
</$set>
\end
In the calling tiddler
<<displaytemplate "MyTemplate" >>
In the MyTemplate Tiddler
<<currentTiddler>>, <<template>>
Regards
Tony