I am a benediciary of a Trust and the trustee wants to transfer the trust to my name shoudl this cost anything?

It is difficult to answer your question based on the limited information provided. It would be necessary to see the trust terms and requirements to determine the best approach and possible cost. It is likely that if the trust is being terminated, there would be some fees charged by the trustee as a part of his or her usual duties. There is not likely a fee to close the trust accounts themselves. There might also be income tax due for income earned by the trust and for the preparation of necessary tax returns.

There are a number of facts that we don't know from your question that might matter. However, there might well be a trustee's fee due upon the termination of the trust. If, the trustee has been being paid during the entire trust administration, that should be minimal. There might also be some expenses such as a fee to prepare a final 1041 and PA 41 tax return.

Finally, as a beneficiary, you are entitled to an accounting of the investments and distributions. However, you might want to work this out informally, as a formal trust accounting might be quite expensive (several thousand dollars) which could be avoided by informally reviewing the trust financials with the trustee.