I like [name]Alexandra[/name] nn [name]Lexi[/name]. I would caution against [name]Alexia[/name] - it is a neurological condition - acquired dyslexia due to brain injury. Bad association.
From Wikipedia: [name]Alexia[/name] ([name]Alexia[/name] from the Greek ἀ, privative, expressing negation, and λέξις = “word”), or acquired dyslexia, occurs when damage to the brain causes a patient to lose the ability to read. It is also called word blindness, text blindness or visual aphasia.
Those who suffer from “alexia” and “dyslexia” can have similar difficulties, however, “alexia” refers to an acquired reading disability, where reading ability had previously been developed, usually occurring in adulthood conditions, while “dyslexia” refers to developmental reading disability.