The determination of the RMD in this case is a bit undetermined at the moment due to varying interpretations of the SECURE Act by the IRS. Prior to the recent issuance in 2022 of proposed regulations, assuming that your grandfather's retirement plan was not a governmental plan the IRS said in IRS pub 590-B that your mother would have been subject to the 10-year rule without the need for annual RMDs, so no beneficiary RMD would have been needed for 2021 but she would have had to complete any uncompleted RMD of your grandfather for the year of his death. As successor beneficiary, you would then continue to follow the 10-year rule being used by your mother with the account being required to have been drained by the end of 2030.
However, the recently proposed regulations indicate that if your grandfather died after his required beginning date for RMDs, the beneficiary is subject to the 10-year rule that requires the account to be drained by the end of 2030 and to take annual RMDs based on the single life expectancy of the beneficiary (your mother). The IRS has provided no information as to whether this regulation would apply retroactively to 2021, but that seems unlikely, so it seems likely that your mother had no requirement to take a distribution from this inherited IRA for 2021. Of course you can find out from the IRA custodian or your mother's statements from this account how much she took from this inherited IRA even though it wasn't a required distribution. When preparing your mother's tax return, when TurboTax asks if she completed all of her RMDs, it seems reasonable to ignore the inherited IRA and just answer with respect to your mother's own retirement accounts (with no distributions required if she died prior to her required beginning date for RMDs).
It doesn't really matter which name you provide as the owner, it doesn't go anywhere on the tax return. All that matters is that the beneficiary in this case is a non-spouse beneficiary.
