If I understand your situation correctly, you will not need to make any changes to your DNS, other than directing them to ns1.dreamhost.com etc. if the domain has not been transferred to DreamHost.
You simply need to tell Apache to serve the site from a directory other than the default. You can do this by changing the ‘Web Directory:’ option when adding otherdomainname.com to the DreamHost system in the panel at Domains -> Manage Domains -> Add New Domain / Sub-Domain.
Another option is not to use your otherdomainname.com, but create a free dreamhosters.com sub-domain and set it to mirror the domain you are working on. See the wiki article below;
Save [color=#CC0000]$50[/color] on DreamHost hosting using promo code [color=#CC0000]SAVEMONEY[/color] ( Click for promo code details )