By that... logic... we should be spelling Jorgenson's name as 'Jørgensen', as that's how it's spelling in the original Danish way.
However, at some point after the family moved to the USA, the spelling got changed to 'Jorgenson'... just like... you got it... the pronounciation.
Of course, if they had made an effort to continue pronouncing their name in the original Danish way - and kept the spelling - that would have been perfectly fine too. But, well... they didn't...
Does it really matter if he pronounces his name differently from, say... Adam Holm Jørgensen?
Of course, in Adam's case he might mostly be using just 'Holm'...