TLDR
WHOIS Privacy services—when supported by the TLD in question—will obfuscate contact information from public display in WHOIS.
WHOIS Privacy in Use
Please note that not all TLDs support WHOIS Privacy. Please check the respective Knowledge Base article to see whether your TLD in question does.
Setup
In order to use our WHOIS Privacy Service, please activate the corresponding appendix first, e.g. through our Control Panel under Domains > Domain Prices > Domains > WHOIS Proxy.
Domain-based (De-)Activation
You can activate WHOIS Privacy for a domain directly in its registration request, or in later updates, the parameter used for this is x-whoisprivacy. Switching this to 0 will disable WHOIS Privacy for the given domain. Changes in the actual WHOIS display may take a few moments to take effect.