One potential consideration is if you want to keep any reviews the client has accumulated. If the old business has a bunch of negative reviews for some reason, and you absolutely want to start from a fresh slate, it might be possible.
here is Google's official guidelines related to reviews transferring over or not.
I'd personally update the listing on Google instead of starting over since I've seen closed businesses that Google associates with you cause unexpected problems before. I haven't seen a case specifically like this recent enough to where I'm sure it's trustworthy for Google in it's current form, but I know in the past having a closed business trailing behind like that could cause ranking issues. Changing the phone number AND the name might make it not matter, but there's enough that'll still be the same (categories, 301s on the old website, etc.) that I'd err on the side of caution.
When it comes to individual citations, you'll need to do what you can, but I'd try and edit in each instance, and only crate a new listing on that particular directory if I had no other choice. If you can't edit an old listing and only have the choice between creating a new one or doing nothing (Yahoo Local as I recall might still be in that category) then I'd just create a new listing, but where possible I'd change it.
Obviously 301 redirects and everything for the old site, to hold onto whatever links you aren't able to get altered to the new site. You'll get slightly more oomph for any backlinks you get updated to the new site, so any really important mentions would be worth trying to get updated.
. New name, new logo, and new website. Business will operate from same office but will have a new phone number.
