A UTMA account is not a trust. It is an account recognized by state law as being opened for a person who is under a disability (age is a disability).
In this circumstance, the CIP FAQ's indicate that the customer would be the custodian, not the minor. You would identify the custodian, but you will still need the minor's name and SSN to meet IRS requirements.
As for filing the CTR, whoever made the deposit goes in Part II. As you surmised, the minor goes in Part I. You would simply note that you do not have the missing information.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.