This is my understanding of Synthentic IVs
You have 2 keys $K_1$ & $K_2$.
$F$ is a PRF
Instead of choosing a separate IV, you instead generate the IV from the PlainText.
$IV = F(K_1, m)$
$c = E(K_2, m, IV)$
You don't need a separate Tag/Hash for authentication. Because the IV is generated using the PT itself, after decrypting the CT, you can generate the IV at the decryption end & check it it's same as IV send along with the CT.
I was looking at AES-GCM-SIV - https://www.rfc-editor.org/rfc/rfc8452
Here the IV seems to be passed as Input to the Encryption Algorithm & is not generated from the PT.
AES-GCM-SIV encryption takes a 16- or 32-byte key-generating key, a 96-bit nonce, and plaintext and additional data byte strings of variable length.
It also seems to produce a tag
Calculate S_s = POLYVAL(message-authentication-key, X_1, X_2, ...). XOR the first twelve bytes of S_s with the nonce and clear the most significant bit of the last byte. Encrypt the result with AES using the message-encryption key to produce the tag.
So why is this Encryption named as an SIV scheme?