Domain name really are just a way of pointing between one server or another. So when you are moving from FASTHOSTS to Mello Hosts you will be pointing your domain name away from FASTSHOSTS to us.
This can be done in a number of ways - the easiest way is this.
When you are sure you have a good back up of your emails
Then you can switch to our servers
Log in to Fasthosts and navigate to your Domain name DNS entries
You will see these entries listed below
ns1.livedns.co.uk
ns2.livedns.co.uk
ns3.livedns.co.uk delete this third entry
You simple change them to
ns1.myecodns.com
ns2.myecodns.com
And then hit save. The movement of your domain name from Fasthosts to Mello Hosts can take up to 24 Hours - you can monitor it's movements as the new Name Servers details are copied to databases around the world,. Use this website https://www.whatsmydns.net to follow those changes
PLEASE NOTE: Only do this when you have everything off your old server on Fasthosts including your website and Emails. There are other articles in the Knowledgebase that can help with that.