I would go for a variation of

• $HTML_Element_obj->{'_tag'}

But consistently shorten HTML::Element to something like HE, to improve readability

• $HE_obj->{'_tag'}

Maybe clarifying that

• $HE_obj = HTML::Element->new(...)

NB: I was assuming that you have to document objects from multiple classes in the same doc.

Otherwise just go for $obj or $elem