You need both a Session messenger ID and an Oxen wallet to get full custody of the name.  Blockchain ownership is transferred to your wallet like an NFT, and then this ownership gives the holder the right to assign what Session ID gets sent messages to it.

For “low risk” customers in a hurry, we will allow you to buy the name and have us assign it to your Session ID without an Oxen wallet, but we do not recommended this because we would still have custody.