Hi Caseyf,
You should see your lawyer and ask if this is necessary. If so, all you need to do is "amend" the will, not make a completely new one. if the will is already executed, then you will need to amend through a "codicil document". This is a document that is executed in the same way as a will, but it refers to the main will, it reaffirms everything written in the main will except to the extent that the will is inconsistent with the codicil (i.e. the new amendments). In the amendment, you can then add "[your niece's former name], also known as [your niece's current name]". However, if you have clearly identified your niece in the original will (e.g. included her date of birth, her address, her ID number/birth certificate number) then an amendment of her name should not be necessary. The whole point is to be able to clearly identify the person without ambiguity. If the person is already clearly identified through other means in the will, then at distribution, the executor/court will try to give effect to the intention of the will maker (you) notwithstanding any slight hiccups in the will.