John McCabe, legal counsel at the National Conference of Commissioners on Uniform State Laws, says Vanguard is right--you cannot name a beneficiary to a UTMA account. UTMAs (so named because they were created by the Uniform Transfer to Minors Act) are not trusts. Rather, when you put money in a UTMA, you are making an irrevocable transfer of assets, and that money belongs to the minor. As custodian, you merely act as a guardian until the minor reaches the age of maturity (usually 18 or 21, depending on each state's laws). If the minor dies before maturity, UTMA money becomes part of the minor's estate. If the minor does not have a will, the parents would most likely inherit the estate.

However, says McCabe, you should be able to appoint a custodian to take over should something happen to you. If you're looking for more information, read Section 18 of the Uniform Transfer to Minors Act ("Renunciation, resignation, death, or removal of custodian; designation of successor custodian.") You can find the entire Act, comments on each section, and information on the adoption and explanation of all uniform laws at the website of the National Conference of Commissioners on Uniform State Laws.