Hi rwyn,
Well, your NI number would be the same even if your surname has changed, so one would expect DWP to be able to work it out. However, they are not best known for putting 2 + 2 together!
A bigger problem is that DWP destroy claimant's old files after a certain time - however, that seems to differ from one person to another! Certainly, after 15 years I would be very surprised if anything of your first claim still exists. For this reason, among others, we always advise claimants to supply all their evidence with every reassessment. If you did not do this then I suggest you send it in when you request a Mandatory Reconsideration.
Nothing on this board constitutes legal advice - always consult a professional about specific problems