The spelling of the name "Bruening" can be explained using the International Phonetic Alphabet (IPA). The first sound, /b/, is a voiced bilabial stop. The second sound, /r/, is a voiced alveolar trill. The third sound, /uː/, is a long, high back rounded vowel. The fourth sound, /n/, is a voiced alveolar nasal. The fifth sound, /ɪŋ/, is the suffix "-ing" pronounced as a voiced velar nasal. Therefore, the correct spelling of this name is "Bruening" with the phonetic transcription of /ˈbɹʊnɪŋ/.