It's entirely personal, but I don't think a person loses their identity because they share a name with an ancestor. At all. If you are already calling her Little Josie, then the answer seems clear-- if you are very worried about the EVL initials, change so that Josephine comes first. Anything else (a new name, etc.) is needlessly complicated when she is already walking, talking, and beginning to understand her own sense of self, as most two year olds are. A total name change to something never heard of before (to her) is much more jarring and identity-shaking than simply easing into using Josie, a name she is already familiar with and that is already a part of her name.
Amy Josephine (AVL)
Amelia Josephine (AVL)
Hannah Josephine (HVL)
Lily Josephine (LVL)
Olivia Josephine (OVL)
Isabel Josephine (IVL)
Charlotte Josephine (CVL)
Mila Josephine (MVL)
Anna Josephine (AVL)
Daisy Josephine (DVL)
Maia Josephine (MVL)
Ivy Josephine (IVL)
Lucy Josephine (LVL)
Millie Josephine (MVL)
Best of luck!
Ooh, also Matilda Josephine - you could call her 'M' or 'Emmy' for short, which would be easier to slip into :) more 'M' names (other than Mila, Millie and Maia that I already posted):
Meg Josephine (my cousin is called Meg... I love it!)
Mae Josephine (I know a 2-year-old Mae who is just the cutest! Her name suits her so well)
Best of luck!
What do you call her by now? If you've disliked the name for this long I am assuming that you've been calling her by a pet name? Maybe you could build off of that, like if you've been calling her Honey you could go with Honora or Melitza? Gemma could be an easy transition, if Gemma Josephine is too much for you consider a 2nd middle in between them? I also think the Ma-J sounds in emMA Josephine could be a good starting point. I think of Magnolia, Margaret, Marjorie. Josephine Emilia or Josephine Emerson, ect could work.
Signing initials really isn't that common. I mean, I mainly see it on contracts and stuff... Honestly. If she needs to sign her initials on some non legal document, she can come up with her own style initial- like the E, circled. But as I see it, her initials are perfectly acceptable as EJV.
As far as monogramming, I much prefer the diamond shaped monogram which is a three-initial design, in which case I'd put EJV. (well, in the order EVJ, since the last initial is the largest in the design, in the middle spot). I understand that Van means something like 'of the'... Such as the o in O' Neil. But in English speaking systems, McDougal is filed under M (or if there are many, the Mc/mac drawer), O'Neil under the Os and Van Diver under the Vs.
Honestly, her name is gorgeous, and I'd go ahead and go on a monogramming spree with the initials EJV. Set her up that way. Honestly I wouldn't even guess her initials weren't EJV.
Personally, I don't think you're overreacting. I saw EVL and immediately got the problem - who wants someone to see their initials and think EVIL?! (Not everyone will see this, obviously, but an equal number of people probably will. As you said, it's already been brought up twice and she's only 26 months old!) I think the suggestion earlier of using Gemma was pretty inspired. Or simply transitioning to the middle name might be easier, since in that case you wouldn't have to worry about legally changing it. OR, as rollo said, using a name that starts with M could still give you the nickname of Emma or Em. If it really bothers you - and it clearly does! - you should change it now, before she gets any older.
You have good taste; Emma Josephine is great! But I can understand why you want to change it, so here are some more names I think you might like:
Avril (prn. like April)
I think you like vintage names (I like vintage eccentric) so these are mostly from that style. Hope it helps! Good Luck : )