Almost all shared hosting plan offers at least one FREE domain registration, some offers multiple with slightly additional fee.
A lot of free “real” domains are offered by web hosting companies. Web hosts will offer free domains with a web hosting package.
Be careful signing up for such service. You may end up with a free domain but a year’s worth of junky web hosting service. The best advice is to keep your domains registered and web sites hosted with different companies.
Finally, seriously consider what domain ownership means. Domain ownership means possessing virtual real estate. Domain names have value and can be bought, sold, traded and developed. They are an investment. Don’t let anyone or anything keep you from true domain ownership even if the offer is free.
I have selected 10 trust worthy hosts from here, which are providing hosting and free domain name while you own the domain name.