The spelling of the name "Boehme" may seem tricky, but it's actually quite straightforward when you look at it phonetically using IPA transcription. The word is pronounced /ˈbøːmə/, with a long "o" sound represented by the symbol "ø" and a schwa at the end represented by "ə". The "h" in "Boehme" is silent, so don't be fooled into pronouncing it like "bohemian". Keeping in mind the IPA transcription, you'll have no trouble spelling "Boehme" correctly.
The word Boehme is derived from the German surname Böhme, which is derived from the Middle Low German word beme or beem. Beme originally referred to a tree, specifically a beech tree. Over time, the spelling and pronunciation evolved, ultimately resulting in the modern German surname Böhme.