Yes. The person handling your mother’s affairs would issue a nominee Form 1099-INT to the trust.
First, try and get the payor to reissue Form 1099-INT to the trust because technically you'd have to file a Form 1041 for your mother to add the interest and remove it.
TurboTax says:
Only interest earned up to that date would be reported on the final tax return. Earnings after that date are taxable to the beneficiary of the account, or to the estate.
That can create some hassles since the payer—a mutual fund, bank or broker, for example—will report income to the IRS on a 1099 form. Although you should try to get ownership of the account changed as quickly as possible after the death of the owner, the 1099 income report may well show more income assigned to the decedent than it should.
In such cases, you'll need to report the entire amount on Schedule B of the decedent's return, and then deduct the amount that is being reported by the estate or other beneficiary who actually received the income.
See Death in the Family.
@cactusjack
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