Name for a Ceasar Cipher that uses random offsets?
In short, it is a stream cipher.

The security of the random number generator is crucial in this design. Also, the key exchange ( the seed transfer) is not defined. To be good use Diffie-Hellman Key exchange and use a KDF to derive the seed.

Modern design is AES in CTR mode where the CTR mode of operation turns a block cipher into a stream cipher and that doesn't require padding. The better use the AES-GCM that provides Confidentiality, Integrity, and Authentication. Another one is ChaCha stream cipher and in Authenticated mode it is ChaCha20-Poly1305.