Op, I'm a Brit living in Caribbean so have a massive mix of nationalities here.
Not once has anyone shown the angst or class snobbery about baby names as people do in the Uk.
If you named your child Avery here, everyone would say "what a lovely name!"
Both my sons have surnames for first names and are in class with Cooper, Hudson, Avery, Aubrey, Tyler, Hugo, Isabella, Huxley, fletcher, reef, kai etc. along with the very popular Ellie, Ella, lily-Mae etc.
In really life, if you introduced your baby as Avery, not one person would raise their eyebrows.
Only in the uk is there such snobbery about baby names. Avery is lovely and perfectly acceptable. Dare I say it, just as acceptable as James or Sarah!