About my website moving and new domainname

It is a little bit complicated, but hope some one can help.

I've purchased a forum, using a sub-domain name like bbs.mywebsite.com.

All the files will be moved to my new dedicated server.

I'd like to use a new domain name for it, like www.newname.com

but still to not lose current memebers, still we want to keep bbs.mywebsite.com working as before.

I have 5 IP availble and want to allocate one of them to the new domain name www.newname.com
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Now, question, what should I do, can some one give me instruction step by step please, to make 2 domains both bbs.mywebsite.com and www.newname.com working properly. don't want to use redirect.

Now what I can think of is, add www.newname.com to my account, and change DNS to point to my nameserver, then copy the whole forum under new website. I dont know if this way is correct. Then I don't know how to link the original forum address to the new space.

thank you very much for your help .