Can I change domain names, but keep sub domains?

This may seem like a silly question, but here’s the dilemma:

I have hosted on DH and wish to move it elsewhere without the sub-domains. However, I wish to host on DH with exactly the same sub-domains that were on Most of the subs are empty now, so no prob but there is one that has a wordpress site.

Must I back this up totally to an offline machine, then re-upload it to the new Is this the easiest way or am I just dazed and confused? What are the steps to change to
[]Back up stuff
]redirect to new host site
[]install new domain on DH
]recreate sub-domains
[*]upload backed up subdomain

Yep, I’m confused. Thanks in advance for any assistance you wish to bestow.