Seed phrases are not "registered" in any sense of the word.
A seed phrase is used to generate private keys. It can generate a near endless number of private keys. Each private key it generates is at a unique derivation path, meaning that (unless you do something very non-standard) each private key is linked to exactly one address for one specific coin type.
Now, taking bitcoin as an example - every single bitcoin address possible already exists. You can send coins to any valid bitcoin address imaginable, regardless of whether or not someone possess the private key which will allow those coins to be spent. The network has absolutely no idea if someone possesses the relevant private key, because private keys and seed phrases are not registered with the network in any way. You simply create them in private, and then use them to later sign transactions. I can create millions of seed phrases and millions of private keys in private if I like, and the network has no idea I have done so.
The derivation path used to generate an address in most seed phrase using wallets is explained in
BIP44. Further,
SLIP44 gives you the registered coin type field number for most altcoins. Because of how this works, seed phrases generate private keys which are unique to each coin.