Much later, near the end of the war. The Ta 152 was the first (to my knowledge) to be named after the designer rather than the company. The late-1944 190D was still designated Fw.
If you read a bit further up on that wiki article you posted:
"Bayerische Flugzeugwerke ("Bavarian Aircraft Works") was founded in 1926 out of the bankrupt remainder of former Udet Flugzeugbau. Originally producing its legacy of Udet-designed sportsplanes, it later went on to secure the services of Willy Messerschmitt, not as a chief engineer but as a free-lance designer. Thus BFW in Munich and Augsburg would produce and distribute designs from Flugzeugbau Messerschmitt in Bamberg. For some reason, (and also in part because of a deep personal animosity between Willy Messerschmitt and State Secretary of Aviation Erhard Milch) the RLM awarded the manufacturers designation not to Messerschmitt but to the BFW firm, and thus Messerschmitt's record-setting four-seat sportsplane design, the M 37, was produced as the Bayerische Flugzeugwerke Bf 108. Dissatisfied with this settlement, Messerschmitt himself used the money from the sales of his designs to buy a tract of land in Regensburg, founded the Messerschmitt GmbH aircraft factory and planned (or threatened) to start aircraft production on his own. Forced to choose between giving Messerschmitt his due and becoming a pure subcontractor, on 11 July 1938 the Bayerische Flugzeugwerke took on Messerschmitt as chairman and managing director, took over the Regensburg plant and renamed itself the Messerschmitt AG. The RLM assigned this 'new' aircraft firm the designation prefix of Me. The first aircraft to benefit from the change was the Me 210. Nevertheless, the three production contract aircraft designs from the earlier Bayerische Flugzeugwerke firm in Germany, the Bf 108, Bf 109 and Bf 110 officially kept their "Bf" prefix, due to their pre-July 1938 origins, until the end."