You can do that by encrypting the names. You send encrypted names to the FHE-server, and then the server does necessary sorting computations on it.

The point of FHE is it can operate on gibberish-looking ciphertext, and when this ciphertext decrypted afterwards, the result is correct.

Indeed, there are those working on faster FHE sorting: https://eprint.iacr.org/2021/551.pdf