could you help me

There are some web hosts offering free domains if you buy their web hosting solutions.

I'd better register domain via Eurodns.com, but the registration is paid.
the company is reliable and I would like to say you can trust them.

free registration is waste. its better you can get registration at cheap rates.

Some hosting companies will give you one free domain name, only if you register an hosting account with them. However, you are the owner of domain name , only if you have an active hosting account with them. You can search the hosting companies via Search Engine. If you want, you can register the domain at a cheaper rate.

I suppose that you understand that those kind of domain names are easy to get but at the same time you can easy lose them one day and all your SEO efforts and other marketing efforts will be wasted. so its better to go for cheap domain registration services. i suggest you Zippozap.com to get domains at cheap rates.