Can I use the same UBC manuscript and put new client names on the cover?

If you plan to create Kindle versions of your Ultimate Business Card book, then selling your own book as PLR probably isn’t a good idea as they are unlikely to approve the books and will remove any that are already there. For KDP Print, you can create Private Label versions of the books with minimal updates if you want to, but it isn’t necessarily what I would recommend.

Instead, I’d set up an appointment with the person to interview them and get their actual expertise and create a book focused around their knowledge and in their words. Just record the interview, transcribe it, and then edit it into a readable format. That will provide the most value for them, rather than having a book that is the same as a dozen others on Amazon. If somebody didn’t want to use their own expertise and just wanted to slap their name on a book, then you could offer to do that but I would not add their book into the Amazon marketplace unless there were some significant alterations. You could still use KDP Print or another print-on-demand company to provide copies of the book for them to use as a UBC without having to have it actually available on Amazon.

Generally speaking, though, I tend to work with people that have some expertise of their own and create a truly unique book for them that promotes their knowledge and works as lead generation for them with calls to action specific to what they can offer potential clients.