I’m looking for a boy’s name to honor an [name]Elizabeth[/name].
[name]One[/name] option is [name]Eli[/name], or a name that shortens to [name]Eli[/name] ([name]Elijah[/name], [name]Elliot[/name], [name]Eliezer[/name]). What else could work?
[name]Eli[/name]/[name]Elias[/name] was my first thought! Maybe [name]Ezekiel[/name]? The only letters that aren’t in [name]Elizabeth[/name] (and aren’t repeated using [name]Elizabeth[/name]'s letters) are one of the "E"s and the “K” in [name]Ezekiel[/name]. It shares a lot of the same letters so I though it was pretty close… That’s really the only thing I can think of right now.
Good luck!
I think [name]Eli[/name]/[name]Elias[/name] would work great! 
Other ones that you might like are:[name]Ellis[/name], [name]Elian[/name],[name]Elliott[/name]?
[name]Eleazer[/name] was going to be my suggestion, but I see you already have it! I think it’s quite similar to [name]Elizabeth[/name] in that it is also of Hebrew origin and has four syllables. You might consider [name]Zabe[/name].
[name]Ellison[/name] is 1 you haven’t mentioned yet. From the one already listed, I like [name]Elijah[/name] and [name]Elliott[/name] the most.
Others:
Eliel
[name]Eligius[/name]
Eliram
[name]Elizeo[/name]
[name]Bethel[/name]
Bethlem
Bethuel
And that is all I got.
Thank you all very much. If anyone thinks of any more, please keep posting - especially any names that start with letters other than E.
A lot of my suggestions are really a stretch.
[name]Bert[/name] (it’s like [name]Beth[/name])
Bettino (it’s a short form Bernadetto, but I think it works to honor an [name]Elizabeth[/name])
[name]Elio[/name]
[name]Abe[/name] (elizABEth)
[name]Abel[/name]
[name]Beckett[/name] (maybe?)
[name]Eliseo[/name]
[name]Ellis[/name]
[name]Lee[/name]
[name]Lysander[/name] (the beginning part sort of reminds me of [name]Elizabeth[/name]).
I looked on behindthename.com and I found [name]Elian[/name].
Meaning, origin and history of the name Elián - Behind the Name
[name]Elias[/name] was my first thought as well! And I love that name!
What about names with the same meaning as [name]Elizabeth[/name]?
[name]Elisheva[/name] (the Hebrew form) means “given” or “consecrated” to G-d. the closest you can come to that meaning is [name]John[/name] (G-d’s grace) or the various “gift” names: [name]Nathan[/name], [name]Nathaniel[/name], [name]Mathew[/name], [name]Matthias[/name], Matithiya. [name]Story[/name]-wise, [name]Samuel[/name] was “given” to G-d by his mother [name]Hannah[/name], just as [name]Moshe[/name] was “given” to G-d by his mother. [name]Just[/name] some ideas.
Maybe [name]Ezra[/name] could work?