Why were you embarrassed? The size is just a letter. It can vary per brand or even in different models of bras.
34DD isn't enormous. I'm a bigger size than that and I've never experienced people staring or not listening to what I say.

Also, I think V necks are actually flattering for a larger chest. Of course you don't want them too low, but as long as they still cover everything up they'll make your chest look smaller.