Cecilia is basically a simplified spelling of
Caecilia, the proper and original Latin form.
As is mentioned in the entry for
Cecilia, the name is ultimately derived from the Latin adjective
caecus meaning "blind" (plus a Latin diminutive suffix, so actually the meaning of the name is more like "little blind one"):
https://en.wikipedia.org/wiki/List_of_diminutives_by_language#Latin (in English)
Names with a descriptive meaning first started out as informal nicknames, usually in order to distinguish two bearers of the same name (think of cases like
Pliny the
Elder vs.
Pliny the Younger). Over time, some of these nicknames began to be used as legitimate given names (and ultimately, family names).
Since the name
Caecilia was borne by
Roman women who lived in the centuries BC, obviously the name and its etymology predate the saint (who lived in the 3rd century AD):
https://en.wikipedia.org/wiki/Caecilia_gens#Members (in English)
Also,
Cecilia was not the patron saint of the blind. Not sure where you got that from. She was the patron saint of music:
https://en.wikipedia.org/wiki/Saint_Cecilia (in English)
Forchta in biuonga quamon ouer mi, in bethecoda mi thuisternussi.
In ic quad: "uuie sal geuan mi fetheron also duuon, in ic fliugon sal in raston sal?"