It’s not always safe to check the availability of domain names on popular domain name registrars and websites like Godaddy and Namecheap etc. The reason is; sometimes unscrupulous people may beat you to the domain name and register it before you do.
There are ways to do this safely:
1. Immediately register a domain name once you check and it’s available
2. Check domain name on the official ICann website. Go to InterNIC Registry Whois Service and look it up.
All the best in registering your new domain name.