Incorrect National Insurance number on my tax code notice letter

I provided my new employer with my correct national insurance number. When I received my tax code notice the NI number on the letter is incorrect and I am also not sure if my first and last name are the wrong way round as well. I contacted my employer to notify them of this error and have been told that I need to contact HMRC about it. Please can you advise how I can get this information corrected on your records. Thank you

Hi Ailsa,
If you could call the National Insurance Helpline on 0300 200 3500 they will be able to check your National Insurance account and provide you a letter to show your National Insurance Number for you to provide to your employer.
Thank you.