While I was looking through marblehost.com web hosting offers I recognized that this company had free domain name within their hosting plans.
Do you think that it will be productive to buy hosting and get free domain name?

Many hosting providers have offers like this. It's useful to check and make sure that you will actually own the domain name and get to take it with you, if you ever need to switch companies.

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Dedicated Server and VOIP Solutions
Premium bandwidth, Solid Hardware
www.pingpipe.com

I have talked about it many times and ech time I still repeat - the only way to get reasonable free domain with hosting account is getting this account at accredited domain registrar. In particular I advise sibername.com

They are offers. So use them if you like it and is useful foremost..

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pest control services | termite pest control

There is nothing as free. It's just a marketing strategy to get more customers signup coz they get a free domain.

you can test their hosting for one month firstly ,if it is reliable and meet your requirement why don't you use it.Also you can ask it clearly ,free domain for life or .......

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Hostease Web Hosting
$o.o1 first month with coupon code TEST
30 day money back+99.9% uptime+24/7/365 support

I may agree with most people here. Getting a domain has to be provided by accredited registrar, and I see no reason to aviod free domains offered by registrars in their hosting accounts, like the suggested sibername.com

make sure that you own the domain once you sign up. Check the whois information for the domain. You can easily do that at a website like iwhois.com

Really the only way to get such domain for free is get the hosting from an accredited domain registrar, which is known for high level of trust. To my mind the offer of free domains at sibername.com is exactly what you need.