Is it considered ethical to sign yourself with name followed by PhD when in fact your doctorate was a DTech? 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.