I would change the name Indians too, and I think the writing is on the wall that they are headed in that direction.
They're slowly removing themselves from the Cheif Wahoo logo. They are now using a stylized C for the most part
Their jerseys have Cleveland in leiu of Indians written across them (only 1 of 4) and I think you'll see that become 2 or 3 next year with the C cap being made permanent.
That's how I'd do it. Slowly, so you don't really notice. Just that you show up to the ironically named Progressive Field and there's no mascot or offensive logo. Have sports networks call them Cleveland and refer to the team by city only. For example, "The Toronto Blue Jays are hosting Cleveland tonight at the Rogers Centre". Once that's all done then changing the name isn't a shock to the system.