How to note that you’re a PhD holder, and should you?

As per title. I just moved to Japan. They provided a Japanese translation of my name in katakana. Should I add something to denote I'm a doctor? In Europe I would say name surname, Ph.D. or Dr. Name surname.

I'm embarrassed to ask my colleagues, and I have the impression they interact with me quite differently than they would do towards Japanese people, this is to say, much less formal (edit: for example they call me by first name and are very friendly when I've seen they use surname and seem more detached for Japanese people).

This is my first week in Japan and I'm quite a beginner when it comes to the language.

Edit: I should specify that I don't mean to change my official name on documents, I'm asking for my email signature or similar things. I'm not particularly fond of titles, as usually my students address me by first name, but in (western) countries I lived before I was previously suggested to use my title in things like signatures etc