You should have told them when you first checked your license after it arrived. As now you don't have a valid license or never really have as the name is not yours on it.
You must inform them straight away that they spelt your name wrong and need it changed. Insurance companies use many ways to get out of paying out and they may use that.
Oh and forget trying to commit fraud as it will get you into more trouble by applying for another license. Plus you would have to take your test again and have zero NCD.
If they've spelt your name wrong you should tell them, but if there's points on it now they'll still be on it when you get it back.
They know every trick in the book.