Re-branding? New domain names questions

I typed in "office products" into Google and found a page with the title,
"OfficeMax" except that the URL wasn't OfficeMax, and it was the second
listing for OfficeMax on the first page.

This is the link:
http://www.boiseoffice.com/

It seems like they don't want to lose their first page ranking but are not
doing 301 or 302 from the old to the new.

Is this acceptable to search engines?

Is it ok to "re-brand" a compay by leaving up the
old site and making a new one, leaving the
old one online at the top of the rankings until the new one ranks?