I am guessing Björn Borg (famous Swedish tennis player) and Björn Ulvaeus (famous Swedish composer and singer who was once part of ABBA) must have played a role in the name's popularity on Malta, just like they seem to have done in much of Western Europe (e.g. Belgium, Netherlands and Germany).
Compare the Dutch popularity statistics for each spelling of the name below. You will see that the name was at its most popular in the late 1970s and early 1980s, at which time both ABBA and Björn Borg were active (the former from 1972 to 1982, the latter from 1973 to 1984).
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Bjorn: https://www.meertens.knaw.nl/nvb/populariteit/naam/Bjorn (in Dutch)
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Björn: https://www.meertens.knaw.nl/nvb/naam/is/Björn (in Dutch)
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Bjørn: https://www.meertens.knaw.nl/nvb/naam/is/Bjørn (in Dutch)
Were the Maltese men that you met aged around 40? If so, then most likely their parents were indeed inspired by one (or both) of the aforementioned two famous Swedes.
Forchta in biuonga quamon ouer mi, in bethecoda mi thuisternussi.
In ic quad: "uuie sal geuan mi fetheron also duuon, in ic fliugon sal in raston sal?"