You must send a reply to UKBA by registered post (keep a copy of all correspondence)
You need to clearly state that they have an incorrect name for you.
You must also state that you came to UK on a Fiance(e) Visa and you have submitted your FLR(M) as such you are not allowed to work so are unable to provide any of the evidences they requested.
Tell them their letter is both disturbing and upsetting, that the person who sent it needs re-training and that you are making a formal complaint and require an apology and a management reply.
Mention that you will immediately seek the assistance and support of your MP and that you will be involving the Ombudsman and the Minister for Immigration. etc etc
By the way once you've sent the letter you must involve your MP and all those others.
You must give this activity priority and maintain a control on this.
What a complete shower.
Don't waste any time composing a long convoluted letter. Keep it short and concise. Even bullet points is enough.