Migrating From domaina.com to domainb.com How Do I Do This?

I have a multisite setup under one domain and it's working great although the project it is being guided under has taken a full name change so I want to migrate it to another domain name with all the same structure that pre-exists.

Is there anything I need to be aware of to make this happen easily? Is there a simple method to this or should I boot the new site raw and just import snapshots?

It's early days on the 'old' site and I only have demo blogs on it so I was thinking to make this easy on myself by asking if this is as simple as just copy the lot // dupe the databases and globally replace the 'old' domain name.

Curious to know how others would go about this.