I like the idea of options. Use [name]Elizabeth[/name], [name]Beatrice[/name], [name]Lilibet[/name], Elsabet- whatever, and call her [name]Betty[/name].
An acquaintance of mine had a baby girl a few months back; first name [name]Betty[/name] (after the family matriarch), middle is another family name, one syllable, let’s just use [name]Don[/name] here, haha. She’s calling her by both, [name]Betty[/name] [name]Don[/name], and when I first heard the name, my immediate reaction was, omg, that kid is so COOL. Lol.
While I think [name]Betty[/name] is adorable, I would also go with the longer [name]Elizabeth[/name] and call her [name]Betty[/name]. I had a conversation on this topic with a friend named [name]Connie[/name] the other day, actually. She said she wishes her parents had named her the more formal [name]Constance[/name] and just called her [name]Connie[/name] so she could use the longer name on resumes. However,she certainly doesn’t hate her parents, just wishes that they had given her more options.
I do love [name]Betty[/name], but it works better as a nickname for me, as it doesn’t seem very formal.
[name]Elizabeth[/name] (or some other longer form) works better as a given name, i.e. comes across more professional.
If the baby I’m having in [name]October[/name] is a girl, she will be called [name]Betty[/name]. We’ll probably go with [name]Bethany[/name] on the BC since it’s the only one DH and I can agree on, but I love the full names [name]Bernadette[/name] and [name]Beatrice[/name] for [name]Betty[/name] too.
[name]Bettina[/name] is another option but I like [name]Betty[/name] and [name]Elizabeth[/name] 
I think [name]Betty[/name] can be fresh & fun, but it feels less substantial for me. It makes me think of [name]Cindy[/name] or [name]Hattie[/name], of course it’s done, but it just doesn’t feel very serious or refined to me. That said, I do love [name]Betty[/name]. I also think a lot of middle aged people won’t be able to move past it being a “grandma” name, at least not until they are charmed by your daughter. Personally, I would use a longer formal name to get to [name]Betty[/name]. I would probably opt for something besides [name]Elizabeth[/name], something more likely to remain as [name]Betty[/name], not be switched to [name]Lizzie[/name] by a [name]MIL[/name] who can’t get into [name]Betty[/name]! [name]Bettina[/name] is perfect! It’s distinct on it’s own, intuitively nicknames to [name]Betty[/name], yet feels more formal & mature if she wants that in a name.
I second what Jesba said. She won’t hate you even if she hate her name.
Me, I dislike [name]Betty[/name] (sorry!) I just can’t see her appeal, but then it’s only me. [name]Betty[/name] is also not a name I like to stand on it’s own, I prefer more formal name. My favourite way to get [name]Betty[/name] is [name]Bethany[/name]. If you choose longer name, she has more nn options.
I’m stark raving mad for [name]Betty[/name]. Please use it! Your daughter will love you.
I favor the [name]Bette[/name] spelling - more glamorous and standalone, like [name]Bette[/name] [name]Davis[/name]. What will you do for a middle name? From your list I quite like
[name]Bette[/name] [name]Violet[/name]. The repeated “et” sounds are pleasing, and [name]Violet[/name]'s sassy purple sings next to [name]Bette[/name]'s retro polkadot beauty.
It is a bit dated to the ears…and unfortunately hasn’t made a comeback. I really like the suggestion of [name]Lilibeth[/name] and using [name]Betty[/name] for short, though [name]Lily[/name] is prettier. Similar names that might work better:
[name]Cindy[/name]
[name]Suzy[/name]
[name]Judy[/name]
[name]Lori[/name]
[name]Sally[/name]
[name]Mary[/name]
[name]Holly[/name]
[name]Lucy[/name]
[name]Melody[/name]
[name]Molly[/name]
[name]Minnie[/name]
[name]Nellie[/name]
Your mother might hate you forever. Your daughter will probably think it’s hip as she will probably be ahead of the [name]Betty[/name] curve by 10-15 yrs.
Thanks everyone, I’m feeling a lot better about [name]Betty[/name] now! I think I would use the full name [name]Beatrice[/name] & not let her know that’s her legal first name until she needs it for a form or something haha.