If you change any entity_id, it will break anything that uses yaml & the old entity_id. Changing the entity name is just changing the name displayed in the frontend.
I should clarify that automations, scripts, etc use entity_id’s
Unfortunately, I don’t know how it got changed. I didn’t deliberately change the entity_id. I’m guessing when things weren’t working, I removed the integration and re-added it (or just re-added it and HA knew it was already there and used the one that was there) and I think that may have changed the naming.
In any case, it makes sense that changing the name would not break things and changing the ID would. But if I changed it, I’m still surprised it didn’t yell at me for that.
To be honest there is so much to learn about the SRM that my mind is a little foggy at the moment. Between figuring out what it does and fixing things that broke and trying to figure out things that still don’t seem to work right, I’m easily confused about everything 
Typically, that will if you don’t restart in between because the previous entity_id is reserved.
I believe there is a blurb on the page, but no confirmation. People usually don’t like extra clicks.