Most likely it's just an inventive spelling of '
Shay' I mean how else are you gonna say it; she? Shy?
Shay would be the only logical answer. I far prefer
Shay and even
Shae.
Heck, even
Shaye. Sheigh looks strange and off putting, to say the least (very reminiscent of that dreaded -leigh trend) it's just very juvenile. I'd be very reluctant to pick up and finish a book with a character named 'Sheigh' (that spelling), particularly if it was the main character.