If a provider is giving out free domain names, there is always a catch to lock you in and make some money out of you. Always read the small print in the Terms & Conditions, especially the termination clauses and rights to the domain name.
That said, I use
Mythic Beasts for name registration and hosting and haven't experienced any problems with them. At the moment, they have domain registration from 99p +VAT (.info for the first year). If you want to splash out .photography (and variations) is available for £18.33.