Yes register.com does offer for free, but bear in mind that their renewal fees is $35/year, you need to ensure you transfer out before then.
When you transfer out, you need to pay the new registrar. Domain names are dirt cheap in today's context and if you want to use it, it is very affordable. Why not just buy it? There are two TLD which offer free domain names. Check out :- http://www.freedomain.co.nr/ http://www.dot.tk/en/index.html?lang=en
www.freedomain.co.nr www.dot.tk can offer free domain if u can't purchase domain now then u should start free blog at blogspot.com so u can place adsense ads there and when u will get money u can purchase ur domain from namecheap.com , godaddy or enom price will be 9.99$ per year.
I respect your question request and i think i said it over 1000 times but you can't get free domains (at least with the meaning we all know , free .com.net.org.....) If you want to create a blog you can do it for free go to blogger or wordpress If you want a redirection account or even basic dns features you already got your suggestions If you want to look professional you can't do it like this As forumers said above there is no point for a registrar or anyone else to loose his money (because they always pay the registry) without any return You will either pay 3x the price with renewals, or they will lock the domain, registrer it to their names, offer it only with webhosting packs..... It's like a walk without any idea where the hole is "FREE" is a very good word and a foundation of what we call internet today but it can also be a trap for people disregard their meaning