Specific name for double PhD
No, there's no special title for such a situation. Someone with a double doctorate still just has the title "Doctor," in prefix form generally abbreviated to "Dr.": "Dr. So-and-So." (By the way, having two PhDs is not a standard stage in most academic careers, and it's not necessarily more prestigious than having a single PhD. See the answers to this question on Academia SE: Is doing two PhD's a good path?)
To specify the type or number of doctorates that a person holds, they can be listed in abbreviated form after the person's name.
Some examples I found using Google:
- Seleshi Sisaye, Ph.D., Ph.D. (text refers to "Dr. Sisaye")
- Bridget Grant, Ph.D., Ph.D. (text refers to "Dr. Grant")
- Xiao-Tong Song, Ph.D., Ph.D. (text refers to "Dr. Song")
At least one senior Nazi in mid-C20th Germany, Otto Rasch, had two PhDs and, according to the Wiki ref below: "was known as "Dr. Dr. Rasch", in accordance with German academic tradition."
https://en.wikipedia.org/wiki/Otto_Rasch
When I was a post-doc in Sweden in the 1970s we had an elderly fellow at Kvantkemiska Institutet with five PhDs (really!), but I don't recall him being addressed using multiple titles.
And the one chap in my dept at London Business School with two PhDs tended not to make a big deal of the first one, possibly as it might detract from his credibility as regards the second one.
I'm not aware of any specific term used for multiple PhDs, unless you count "Professor" or perhaps "Egg-head!"
Thanks for Comments below, regarding which:
1) I agree that we tend not to use double titles for doctorates in the UK, but as pointed out, some titles are combined here:
2) While I cannot locate a German source for how Otto Rasch himself was addresssed, nevertheless as given in https://en.wikipedia.org/wiki/Doctor_(title):
"In Germany, double doctorates are indicated in the title by "Dr. Dr." or "DDr." and triple doctorates as "Dr. Dr. Dr." or "DDDr.". More doctorates are indicated by the addition of "mult.", such as "Dr. mult.".