29 Sep 2016 3:05 PM:
I had the same issue. Eventually after several fruitless trips to the local office in Cartagena - arriving early, queing up (no appointments given) - I discovered that the only place it could be changed was at the office at which it was issued in the first place. That happened to be the Consulate in London. Once I discovered that I managed to make contact with someone there, who eventually sent me the relevant form to complete (in duplicate, naturally!). I went down to London, paid (I think) £7.50 and it took about 10 minutes. And yes, it's because in Spain you don't change your name on marrige, but because I did and I changed my passport into my married name when it expired, I was told I had to get the NIE changed in order to pay my non-resident taxes (though i queried whether the authorities would have refused to take my money because I paid in my maiden name).
Forum thread:
Changing name on NIE
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