Bjoern

"Bjoern" isn't really a name - "oe" is sometimes used to represent ö and ø when those letters aren't available for whatever reason (like on a keyboard), but even when the letters aren't there it's more common to just spell it "Bjorn" without the ö/ø and as far as I know "Bjoern" is not an actual form of the name - but I could be wrong!

Anonymous User is right: this name is not really (or if so, very rarely) used in German-speaking countries (the German form is Björn). You will, however, sometimes see Bjoern in contexts where the letter ö does not exist, would confuse any international counterpart (for example e-mail addresses) or in contexts where it might be necessary to "internationalize" the spelling. [noted -ed]