Moving SQL DB's From Machine To Another With The Same Name

hello everyone. i am new to the group so i aplogize if this question has
been answered recently...

our sql db machine is too old. we bought a new server with which to replace
it. the trick is, we want to keep the name of the machine and db instance
the same.

obviously, we don't plan on having two machine with the same name on the
network at the same time. how do we handle this?

my first thought is to name the new machine with a new name (mach2),
transfer over all the db's, take the old one (mach1) off of the network.
rename the machine/instance to the old one (mach1).

if i do this, can i drop the original instance on the new machine
(mach2)-->register the new (mach1)? will my data be there?


Thanks so much for any relplies!!!