The network does not obtain your private key. That is why it is called "private", and this is the whole reason that digital signatures are secure
When someone pays coins to you, the transaction includes your address, which is a hash of a public key. Public keys and private keys come in matched pairs, and to spend the transaction, you create a new transaction that is digitally signed using the corresponding private key. The signature incorporates your public key, and anyone on the network can verify that it is valid. A valid signature cannot be created without access to the private key, but the private key is not part of the signature and cannot be recovered from it.
If future transactions are paid to your address, you're still the only one who can spend them, so long as you keep your private key secure.