Is it considered ethical to sign yourself with name followed by PhD when in fact your doctorate was a DTech?
Ethically, you should portray yourself accurately. So don't say PhD unless that is your degree. It might even be considered, by some, as an attempt to defraud.
If the DTech degree stands on its own, then there is no issue with using it. But if some consider it a "lesser" degree then they would interpret saying PhD as an attempt to give yourself a promotion.
So, not only an ethical issue, but a practical one.
Note that the US NSF has definitions of which degrees it considers "research doctorates" and hence "equivalent" to a PhD. But not that they are PhDs.
Of course, for usage outside the US, there are different conventions. If the country in which the degree was earned considers the degree to be equivalent then it is, but it still is not a PhD. Be accurate. When it matters, you can, of course, explain the background.
However, DTech is a bit tricky since it can be a higher level (than PhD) degree from some UK institutions, but a lesser level degree from others. Higher-level degrees normally require a doctorate be earned previously.
Of course it’s unethical. Misrepresenting your educational credentials is always unethical. The details of why you rationalize doing it are irrelevant - if you don’t have a PhD, don’t write the letters “PhD” after your name. For example, a friend of mine has a doctorate in mathematics from Oxford. Cool, right? But guess what, he doesn’t have a “PhD”, he has a DPhil, so that’s how he signs his name when he wants people to know about his doctorate.
Edit: the comments below go into lengthy discussions concerning the precise nature of the distinction between the PhD and DPhil degrees. This may be an interesting question, but is off-topic and has no bearing on OP’s question or my answer to it, because: first of all, OP asked about a DTech degree, not a DPhil; secondly, my answer addresses the specific context of signing your name “firstname lastname, PhD” when you have a degree other than a PhD. In that context, a person signing their name that way is engaging in an obvious misrepresentation of their educational credentials. As I said, intentionally misrepresenting such information is unethical, and I would advise against it.
As for other contexts such as a casual conversation with a family member who doesn’t know or care about the minutiae of various academic degrees and their significance, my answer might have been different, but that’s not what was asked about so I see no need to discuss it.
In general it is a misrepresentation to list a kind of degree that you have not earned. The best way to list the degree is as it was awarded by the institution from which it was earned: if it's a "DTech," list it as a "DTech"; if it's a "DPhil" or "PhD" list it as "DPhil" or "PhD", respectively.
One other thing to consider is that in some countries—particularly in Central Europe—it is not only unethical but illegal to misrepresent one's credentials and to misuse titles one has not earned, so it is better to err on the side of caution and not claim anything for which you do not have "hard" documentation.