Sound-by-sound transliteration of 'Ja-mi-son':
贾 (jiǎ, also a Chinese surname) +
米 (mǐ, 'rice', commonly used for 'mi') +
森 (sēn, 'forest', a standard choice for the English '-son' ending, as in
杰克逊 Jackson uses
逊 instead, while
森 captures '-son'/'-sen').