M name has changed legally and I cannot find where to update it. Please help.

Use any internet browser and log into https://appleid.apple.com/#!&page=signin and then click Edit (near the top right of the screen) in the Account section.

Log into your Apple ID and in the first section tap/click Edit. You can change your name there. That will not change your @iCloud, @Mac or @mw addresses. They can't be changed.

Apple ID - Manage