Is there any way that I can own a domain name without paying for it ?

[Jake]

No there's a hard administrative cost to any decent domain names. As mentioned they are commonly included in hosting package bundles costing around $8 a month ($96 a year) and cost the same in following years.

You can find .info names for $2 in the first year, some believe they end up taking a year longer to get decent search ranking.

There have been occasional free domain names, but they are trouble worse than a subdomain, Google actually banned 11 million free co.cc domains from their index because too high a percentage were used for devious purposes, too easy to use in risky schemes.