Hi there!
Just for reference, there is a post discussion here
http://talk.uk-yankee.com/index.php?topic=68562.0 on that very topic.
But to sum up: Seems different people had different results when they applied for their NIN. No one that I read of has posted about trying to get their name changed, so I would say, ask them about it.
Some people got their NINs under their maiden name (same as their passport/visa) and others (like me) received their NIN cards with their married name, even though the passport/visa has their maiden name. I know that for me, specifically, the lady putting my form through, wrote out that that my married name is what I am using now, so I would like my NIN in my married name. I don't know if that was the case for you.
Also, several people have posted that even though their NIN was in their married name, they simply supplied their employer with their marriage certificate to copy and all was well - everything with the employer was in their married name.
I can't say this is a guarantee for you, since people have had several different results through the whole process. But if you are able to get it changed, please let us know!
Good luck!