Seperate to what?

There are a number of domain name registrars who you can work with.

Could you please provide some more info on what exactly you want to do ? The nameservers can be provided to you by the web hosting provider you opt. The domain registrar will only register your domain name.

Godaddy are a domain name registrar. They are fairly competent i guess.

I always look for the cheapest of the lot and go there.

You can choose a good domain name registrar such as godaddy, Namecheap or 123-reg.

I know only Eurodns.com which I've used several times to register some domain names. They are offering affordable as for me services and great support, I like them

I believe that you should look for reviews on their services. From the personal experience I suggest you to give a try to Eurodns which offers are perfectly fit for any webmaster with their quality and cheap offers

Godaddy is the biggest registrar, they can be trusted.

Hi, There are a big number of reliable domain registration services and you should define with your domain extension and budget.
I strongly recommend you Eurodns solutions which are provided with helpful support for affordable pricing

Your question is not clear to what you want keep your domain name separate? and yes Dodaddy is the most popular registrar these days.