Anna is so classic and well used internationally that I'd personally be looking for something similar - I'm assuming you've googled all the "classic" baby name lists on name websites?
Something like James, Edward, William, Henry, Charles, Thomas, Jacob, Benjamin, John, David, Robert, Alexander, Samuel, Michael, Matthew, Daniel, Joseph, Adam, Luke etc for boys.
Or Isabel, Elizabeth, Eleanor, Alice, Maria, Sarah/Sara, Emily, Alexandra, C/Katherine, Charlotte, Caroline, Laura, Julia, Eve, Rose, Lydia, Victoria, Rachel, Rebecca etc for girls.
I do actually really like Rufus, Tess and Cora as well as Barnaby, Laurie (if a nn for Laurence) and Rosamund but I wouldn't automatically associate their style with with Anna iykwim - although I suppose the first 3 have a similar short/simple feel to Anna. In which case maybe Owen, Evan, Hugh, Lucas, Lara, Nina, Rosa?