The choice of aircraft had nothing to do with Göring in a personal sense. The problem was within the RLM- Reichsluftfahrtministerium (Air Ministry). Erhard Milch and initially Ernst Udet before his death were the controling influences in it.
The Bf in Bf 109 comes from the 1925 merger with WW I, 62-kill ace Ernst Udet's Bayerische Flugzeugwerke. As of 1932 Messerschmitt was the sole owner thanks to a huge loan from the Air Ministry. Early Messerschmitt aircraft retained the Bf in their designations like the Bf 109 and 110.
Udet was personal friend of Willy Meserschmitt but a long-standing mutual dislike between Messerschmitt and Milch stemmed from a 1928 incident. Göring liked Messerschmitt perhaps only because he disliked Milch more so and gave Messerschmitt favor.
The real tragic figure in all this was Ernst Heinkel who was virtually made a persona no grata because of his criticism of Htiler and the RLM. He was pals with Udet though. Why did they dislike him so? Because in 1939 he was extolling the virtues of the jet turbine and no one wanted to hear it from Hitler to Milch. Here is the very thing that we all discuss in "what if" scenarios- early jets and producing plenty of them, and Heinkel saw the future and wanted to push their development.
While Herman Göring led the Luftwaffe his intermediary was the RLM that took his want list and attempted to make it reality by interfacing with manufacturers. If a certain type of aircraft was desired Göring would put down the specifications and the Ministry would draw them up as technical requirements and pass them on to aircraft builders. Of course people from the higher echelons of the Luftwaffe contributed what they envisioned as needs too. If the manufacturers thought they could create the said aircraft they presented a proposal to the Ministry with as specific as possible performance data, based on their expertise. The "P" before most numbers stands simply for Projekt. When a project was accepted a company designation number was attached.
As the war unfolded the Air Ministry would put forth specification criteria for aircraft that they in their alleged expertise thought Germany should have.
In the latter stages of the war Albert Speer headed the ministry due to his ability to generally keep all German industry humming. Aircraft requirements were now concentrated on interceptor types. Sometimes balanced designs were compromised or deliberately overlooked for unknown reasons while some planes were built that had little value. Promising types were more often not considered.
Such is the case if one tries to open the champagne bottle, fussing with the cork, at a minute to midnight on New Year's Eve.