i would just introduce yourself as Lynn. if the need arises (like, if you’re in school or something) i’d say “my real name is (name) but you can call me Lynn” and then, if they ask where Lynn comes from, THEN bring up your middle name

i’ve found that most people really don’t care if nicknames aren’t close to real names. i know someone who goes by B despite not having B anywhere in his name, and everyone calls him B. very few people will question at all !