After you file

I mis-spoke. Instead of 'trustee' I should have said 'beneficiary'. This beneficiary received a Sched K-1 from the trust with her incorrect legal name on the K-1 (and corresponding K-1 equivalent for the state). So, should I (as the one submitting the 1041 & K-1s to the IRS and the state dept of revenue) try to correct this pro-actively, or just wait and see what happens re-actively? If I try to correct this, how is that done? Also, can or should this beneficiary do something to correct this situation at her end with her tax accountant?  Thanks for your thoughts on this.