For future readers:
Note from the future: In 2024, the HTML TAG style does have a box for user-defined keyword slots. I don’t remember when it was added, but it’s been there for a while now (I can guarantee at least since v8.6.6, but I think a lot longer than that). So if you want this, start by upgrading to the most recent Notepad++.
Further, as I say here, I recently learned that the HTML lexer has the ability to enable “substyles” for the HTML TAG style, which you can assign your own color and your own list of keywords – so you could style your custom tags differently than the builtin tags if you want. Unfortunately, Notepad++ doesn’t (yet) enable those substyles, so you cannot do it natively in Notepad++. In this post, I share a script for the PythonScript which enables substyles – that specific post gives the example for PHP, but if you want to do the same for HTML, you would follow the same instruction, except edit the lists in class HTML_SubstyleLexer and append your colors/list definitions to the SCE_H_TAG in that class’s colorize.