Anonymous Wire Transfer

It is not possible to make anonymous wire transfers /swifts.

The only solution would be, that you register a company name and account with the current bank and make the wire/swift from your company account. I that case, the only name that would appear is the company name.

Bank-to-bank wire transfer is considered the safest international payment method. Each account holder must have a proven identity. Chargeback is unlikely, although wires can be recalled. Information contained in wires is transmitted securely through encrypted communications methods. The price of bank wire transfers varies greatly, depending on the bank and its location; in some countries, the fee associated with the service can be costly.

Wire transfers done through cash offices are essentially anonymous and are designed for transfer between persons who trust each other. It is unsafe to send money by wire to an unknown person to collect at a cash office: the receiver of the money may, after collecting it, simply disappear. This scam has been used often, especially in the so-called 419 scam.
 

What is an International Payment?

International Wire Transfer

SWIFT MT 103 Basic Format for Wire Transfer

List of SWIFT Codes Worldwide