I personally wouldn’t shorten [name_f]Eliza[/name_f], but what knocked it off my own list was the possibility others would, as I really dislike [name_f]Ellie[/name_f]. I think [name_f]Ellie[/name_f] or [name_f]Liza[/name_f] would be the most likely diminutives if any. I don’t think [name_f]Liz[/name_f] / [name_f]Lizzy[/name_f] is likely as the vowel sound is different - it makes sense for [name_f]Elizabeth[/name_f] as the vowel sound is the same.