You should Register your domain name with a registrar and host the site with another?

First of all it is important to note that you can actually host your site with a registrar and keep your domain name with another. I want this clear because I remember the trouble I had to find a direct answer to this question when I built my first website.

Secondly, do not expect anyone to go out of their way to make it easier for you to do this. I am at least average intelligence, but every time I try to host my site in a register other than the registrar becomes a little 'discomfort. Whether it's an inexplicable 24-72 hour waiting for a switch or forgotten or support personnel who tells you there's a computer error, something unexpected turns up to frustrate you. Why? Someone will say it is because the registrar wants to make it as difficult as possible to change the host website. Frankly I think it's less a matter of greed registrar that the complexity of the system itself. Working with various support groups I've never felt consciously hinder my movements, but often I felt they were not sure what to do next. Each registrar appears to have a different control panel and levers all have different names - or so it seems.

But with a little 'patience you'll be fine and your site will be up and running as good as if I had left the site with your domain name registrar.

So, why bother to register with a registrar and host with another? Some developers think it's a good idea to separate the two and limit the control of any registrar on your site, but the only reason I ever had the good sense to me was money. Sometimes you can get domain registrar or hosting a lot cheaper than another. Often the price difference is enough to make the effort worthwhile.
Cheap Domains and websites at low cost are always worth trying!

So the answer to the question to you in the title of this article is perhaps a possible strong! ......