You may want to either use:
Check this for reference:
It won't really merge the 2 accounts but, at least, the customer will continue having notifications on the same GMail account.
Hope it helps!
For anyone interested, I'm testing out an app on the app store that would allow store owners to keep track of duplicate customers and merge orders placed by them. I plan to keep the app entirely free since this issue seems like such a pain-point for folks.
I'd love help to test the app out in its alpha stage! For those interested, please sign up here and I'll be in touch when the app is on the store: