Prof. Dr. Jan Jürjens - My name

You may leave out the funny dots if not available: Jan Jurjens
In German it is customary to substitute ü by "ue" when Umlauts are not available: Jan Juerjens

In .html my name is written Jürjens, in TeX J\"urjens.
Unfortunately, bibtex doesn't properly handle non-ascii letters when creating citing abbreviations in the alpha style, so there you need the slightly complicated-looking:
author = {Jan {J}{\"{u}}{r}jens} (except if there are at least three authors to a publication; I promise I try to make this happen more often to simplify things).

Note for searching citations etc. in public databases: Most citation search machines do not seem to be able to deal with the Umlaut in my name. A query which approximates the correct result is linked here.

Popular misspelling: Jan Jürgens (with variations Jan Jurgens and Jan Juergens).

By the way, in German, Jan is a male first name (as opposed to the English female usage).

Now that you got this far, you are ready to start trying to pronounce it.