1. Point the domain name from 123 reg to your evohosting server space.
2. Move the name from one host to the other.
For a name to be visible on the internet it must be hosted, rather than just parked. My advice is that you move the name to evohosting.Some hosts are not particularly helpful when it comes to transferring names away to another host - they'll either charge you to do it, or make it difficult for you to achieve. I'm not suggesting that this is the case with 123 reg, but a quick look at their site didn't provide me with any indication that you can use an automated process to transfer a name out.
The mechanics of a transfer are as follows:-
You obtain your new host's IPS Tag - this is a unique code that identifies your host to the DNS servers around the world. Each domain registration company/web host has an IPS Tag.
You then contact your current domain host and ask them to change the tag on your domain name to the one you've obtained from the new host. Some hosts require a fax confirmation of transfer requests.
You tell the new host that you're transferring the name, so they can associate it with your hosting account - this is often an automated procedure.
The transfer should occur within a day or so, and once it happens you'll find that your web site will appear on the internet - usually around 24 hours after the actual transfer. There's nothing to stop you building your site in your evohosts server space while all this is going on, but it won't be visible on the internet.