Who can help? What is the correct designation or from when to when were the machines named Bf 109 or Me 109 and why?
In the year 1938, the "Bayerische Flugzeugwerke AG" (BFW) was renamed "Messerschmitt AG". Willy Messerschmitt was the chief designer at BFW. The Bf 109 was still designed and constructed at BFW - that's why the aircraft has the designation Bf 109 (Attention: Always without hyphen!). Aircraft that came after BFW took over then had the designation "Me", like the Me 163 or the Me 262.
In Switzerland, the Bf 109s were designated Me 109 from the beginning, a designation that the aircraft didn't actually have - but somehow then was obvious, since they were designed by Messerschmitt and built by Messerschmitt.
The German aircraft never had a hyphen in their designation.... and the second letter was always lower case. So Junkers Ju 52 and not Junkers JU-52
Bf-109 oder Me-109