Lee - to be honest, no. It does matter that you get your name from a honest registrar, so you actually own it. There are a few out there who have scammed and they own the domain, and let you use it, as long as you host with them. Change hosts, no more domain.
Also, be aware that *all* legit domain activities pretty much take place by email - not postal. Wife got scammed for $50 last December 'cause one of the scammer sent something in the mail relating "to your domain gruv.org and indexing". They were supposedly a search optimization site, but of course they never did anything beyond cash the check...
When you buy the domain, you'll need to define a primary name server and maybe a secondary that will be the authority for your domain, and in turn those 2 machines (or one machine with 2 ips) must have a DNS service listening that will respond with answers for your domain, any sub domains ( pelicanparts.com is wayne's domain,
www.pelicanparts.com is a subdomain, as is forums.pelicanparts.com ), and optional things like where email to user@domain should really be sent (mx records or mail exchangers).