phil; wrote:... our signature is our unambiguous agreement and any transaction where it is required and offered and used, legitimately, is a contract.
This is the way it is, you sign you agree.
WHY?
phil; wrote:...[Your] Signature IS, after all, your 'MARK' and the use of your name in a signature is 'NOT' required...
The convention IS to use your name, but like I say it is not a requirement it's just the norm. However regrdless of what you put in the signature box you WILL be contracting.
phil; wrote:The solution where signature is required, by intimidation or other, is to incorporate Under duress as part of or used as your signature.
Signature IS after all your 'MARK' and the use of your name in a signature is NOT required. SO write in signature form 'Under Duress', or 'U Duress'. This has the same effect as a copyrighted signature, in a court they will have to accept and use their laws that understand you have given consent under duress.
Your signature is not the problem here, you can sign anything so long as you agree to all the rules / statutes / acts etc.
What is it that you feel you are / would be signing that you don't agree with?
In the contract, your application, you can cross out and initial all the sections you do not agree with and if they accept it you have altered the contract to your satisfaction. If they don't agree they will send it back and so goes the story.
This is a contract and you have a say in what you wish to contract over, Can they flat refuse? Suppose so, but you could try, they might just rubber stamp it without noticing. Then again there may be a freeman 'type' in the system that knows what you are doing and just let it through. Stranger things have happened.
Mostly the DVLA chaps have a 'BORING'

job and posibly never read anything it's why it's termed rubber stamping.
Let us know what you decide to do and if you get a result or responce.
Namaste, phil;