The devil is often in the detail, and you have mostly avoided managing to post any relevant details.
The date you received the SJPN is all but irrelevant. What matters is the date of the Written Charge and Single Justice Procedure Notice.
Assuming (usual caveat applies) that the underlying allegation concerns your vehicle, the only relevant thing is the address on your V5C (or any changes that the DVLA were processing, variously at the date of the alleged speeding offence or the date (or the day before the date) they looked up the keeper details to send the NIP.
You have told us that the SJPN is in your old name, but have not told us whether the address is correct, or on "the letter" that you mention (presumably a copy of the NIP???).
As it stands, and assuming that none of the details you avoided troubling us with are of any assistance, you cannot be convicted of the speeding (unless you plead guilty to it), but you would be convicted of the s. 172 offence unless you can convince the court that (on the balance of probabilities) the NIP was not delivered.
If you plead not guilty to both, you would have the option of doing a deal with the prosecution (or possibly the court) to drop the s. 172 charge in return for pleading guilty to the speeding. If you plead guilty to the speeding, they might simply drop the s. 172, or they might not - potentially leaving you facing the points and fines for both.
N.B. If you decide to "do the deal", do not mention that the NIP was not delivered - as that would be a defence to the speeding charge and the court would be obliged to disregard any guilty plea.