Goering wouldn't have even tried to make that run. We're talking Goering here. The last time he had to go on a run was during the Beer Hall Putsch, and he was much younger than and far less delusional. 1945 Goering does not think he did anything wrong. "Hiding is for those bastards with runes on their collar tabs, my conscience is clear. Oh, sure, mistakes were made, dear chaps, and yes, yes, there were unpleasantries on the Eastern Front, but I mean, really, we're talking Ivans here, not real people, eh, and besides, that was Himmler's boys and - and you did not hear this from me - some of the lads in the army did some, uh, things you would not want to read in the papers as well. But I ran the Air Force - we were clean. Show me one Red Cross I bombed! Show me! Anyway, enough of that. Here is my ceremonial sword. What's for lunch?"
Also, from pure mechanics of it, how does Goering hide? We're not talking some faceless functionary here. We're talking the second most famous Nazi. He'd be the first to tell you that part as well. And as I said, there's the personality. Goering cannot simply grow a mustache, drop some weight and spend the rest of his life calling himself Frederick Miller, the friendly cabbage farmer down the road. He'd rather chug fox feces than pretend to be another man.
It hurt Goering's bones to have to mend fences with Hitler late in the war and debase himself by saying cringe-inducing things such as "When I speak, it is not I who speaks, but Hitler speaking through me" so it would get reported back to Hitler that he is loyal. Towards the end of the war, he resorted to having minutes of Hitler's many, many monologues during the war time discussions be given to him, so he could verbatim repeat Hitler's points to further prove his loyalty. It near broke him. And now, free from the shackles of the only person greater than him that he can acknowledge, he's going to hide under an assumed identity? "Why? The Leader is dead. The pretenders to the throne had the decency to off themselves. I am the Nazi Movement! Who better to take up the mantle of leadership and settle things with the Allies and ensure a proper accounting is done? Name one person! I dare you! Let us not pretend Ribbentrop can speak on the same level as I. All knew I ran the foreign policy. Rosenberg speaks for nobody but the voices in his head. The Army does what we tell them. Speer is a nice enough fellow I suppose, a good order taker. As for the rest? I mean, really, Robert Ley? Or that pathetic creature Streicher? Oh, very good, some Admiral got named the Leader at last second. But come now, this is not a serious discussion. I am the living embodiment of the Party and the State. Ask me anything."