Phonetic transliteration of the English name Jesse / Jessie.
杰 (jié, 'outstanding') captures the /dʒɛ-/ onset;
希 (xī, 'hope') stands in for the /-si/ ending. Both characters are common in Chinese given names too, so
杰希 reads naturally rather than feeling 'foreign'. Note an alternative rendering
杰西 is also common.