I have this same problem. Our surname is a descriptive word so when it is Lastname, Firstname it can sound pretty silly.
With your baby Berry, I think there a lot of names that will work - just not word names.
The Berry's that I know have regular names. Dave Berry, Rachel Berry, Diana Berry, Halle Berry (I guess that one isn't a common one)
I am sure you will find something you like.
Here are some that could work for girls:
Estella - Stella
Alanna - Lana
Elisabetta or Isabetta
Here are some for boys:
Nathaniel or Nathan - Nate
I think the only one for girls that works is Zetta. Zetta Berry. Although that sounds kind of like a berry... Delaney would be to much -ee with Berry.
For boys, Weston Berry is the only one I think sounds good. The rest either sound like a type or Berry or just don't flow the way I'd like...
As for names, I think nouns are definitely out, it would just sound too much like a fruit or yankee candle. In terms of flow, definitely 2 or more syllables sounds better.
So my suggestions would be: