I think for most people it tends to be some names that end with an ee sound - Toby, Lucy, Emily
Nicknames ending with ee (ok for a nn but twee for a full name) - Rosie, Tilly, Freddie, Alfie
Some flower names - Lily, Primrose, Lavender
Some Victoriana names - Elsie, Mabel, Albert
Clearly not all of these - Henry, Rory, Mary, Verity don’t sound twee, nor do Rose and Iris, or Arthur and Edith. But if you avoid the categories above you will probably avoid twee.
I think names like Lexie, Hallie, and combos like Tilly-Rose, Trixie-May are regarded as both twee and downmarket.