I LOVE he name Eliza! If you wanted a more meaningfull middle name, try playing around with your mothers name or grandmothers names. You could also use the month of her birth,
Eliza September Bowen
Other than that, some names that just sound pretty are
Eliza Denise Bowen
Eliza Kate Bowen
Eliza Michelle Bowen
Eliza Renee Bowen
Eliza Katherine Bowen
Eliza Margaret Bowen
Eliza Jane Bowen