Hi @Roger Roger ,
Good day, welcome to the Microsoft Q&A platform!
Based on your description, the issue occurs if you're not a manager of the group. Even a user with global administrator can’t remove or make a change to a distribution group. The fact that you are not the distribution group owner could stop you from completing the required management task as my test in screenshot below.
To fix the permission issue, you can add the -BypassSecurityGroupManagerCheck parameter to the PowerShell command as my test below. Then you could add the owner to Distribution List successfully. And you can add multiple owners after ManagedBy.
Set-DistributionGroup -Identity "xxxxx" -ManagedBy "xxxx" -BypassSecurityGroupManagerCheck
If the answer is helpful, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".