Her last name 水橋 (Mizuhashi) means 'Watery Bridge'.
According to ZUN in an interview in Cara☆mel released with CiLR7, the term 波斯人 (hashihito) refers to Persians, and he thought it would be interesting to try to make a Persian hashihime in old-style clothes...even if she doesn't really look like a hashihime.
The name of Parsee's boss theme, "Green-eyed Jealousy", as well as her midboss spell card, "Green-eyed Monster", are both terms used in Shakespeare's works to poetically describe jealousy.
Due to her picture in Subterranean Animism, she is often depicted having elf-like ears, even though it was not on purpose at first. Since she was the first character with visible ears, ZUN had trouble drawing them.