How much does it cost to have a codicil drawn up vs. just changing the entire will. I just have to change the name of the one beneficiary.

It depends upon your current Will. How and when it was drafted. Wills can be simple or extremely complicated. However, in Texas, if you had a Will drafted and were subsequently divorced, then your former spouse will be treated as if they pre-deceased you.    Texas Estates Code: Sec. 123.002. TREATMENT OF DECEDENT'S FORMER SPOUSE. A person is not a surviving spouse of a decedent if the person's marriage to the decedent has been dissolved by divorce, annulment, or a declaration that the marriage is void, unless: (1) as the result of a subsequent marriage, the person is married to the decedent at the time of death; and (2) the subsequent marriage is not declared void under Subchapter C.