In Germany and Austria¹, it is possible to have your doctoral degree noted on your passport, official ID (Personalausweis) and similar documents of identification. Whether allowing this is a good thing in general is debatable but the subject of another question (that is arguably too opinion-based for this site).
Having acquired such a degree, I fail to see any strong arguments for or against making use of this as an individual (and the Internet does not provide much searchable information on this issue either). Obviously, it flatters the ego and can be used to impress some people, but then it involves some effort and may come off as arrogant to others. But I am wondering whether there are some situations where there is a more clear advantage or disadvantage or whether I am grossly misestimating the situation.
Note that I do not ask you to make this decision for me. I am fully aware that I have to weigh the advantages and disadvantages myself. I am just asking for arguments.
¹ which seem to be the only countries where this is possible if some websites are to be believed
Finally, for the search engines: Was sind die Vor- und Nachteile davon, seinen Doktorgrad im Personalausweis vermerken zu lasen?