First off, if your supplier has not already got CE marking then I would agree with MIREGMGR, it probably isn't worth the pain and effort for a class III product.
If the supplier does hold a CE mark for the product then there are a number of options open to you and your decision depends on how much pain you can tolerate and how why you want your name on the device
1. Own label.
If you want to be the "manufacturer" and have only your name on the device then this is the way to go. Even though it's a class III because you essentially rely on the original CE mark, it is relatively easy to do. That being said, I wouldn't recommend this route if you do not hold any other CE marks > class 1 and don't have systems in place to meet the requirements of the directive. It will also require a lot of cooperation from your supplier and you should be sure to understand the implications of being the legal manufacturer.
2. Brand the device
If own labelling is unappealing, you can always stick your own name on the device and leave the small print to state who the manufacturer is. As long as the manufacturer is clearly identifiable then there isn't too much of a problem with this, it's best to work with the manufacturer and their notified body to smooth out any wrinkles though. I have in the past seen products were unless you know what you are looking for and looking really hard, you wouldn't be hard pushed to identify the legal manufacturer.