What is this technique called? There must be a name for it.

Well, this technique resembles what the ol' CGI.pm was doing in its days. I would say that it is against the DRY principle in software development - Don't Repeat Yourself - so whilst it might have a name, it surely is not a flattering one. Writing

add_h1('Title');
add_p('Here is the opening paragraph.')
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requires two functions, while writing

add('h1','Title');
add('p','Here is the opening paragraph.');
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requires only one, which means less code and a smaller memory footprint, at the expense of typing 2 more chars in the source for every call ('' against _). So, having a function for every tag is overkill, as haukex correctly points out.

There are plenty of ways of generating HTML code in a more flexible way, e.g. Mason (before and after going the Moose way), Template::Toolkit and other templating solutions.

For more overkill, but with the benefit of writing HTML in a perlish way, see Re: Perl module for RELAX NG? (shameless plug) which converts every tag of a DTD to its function, which takes a block as first argument. I use it only to write templates to be processed by a templating engine, since it is pretty slow. See also Which internal DSL are there in Perl? (Domain Specific Languages - Part 1).