How to rename a doctype, if renamed will all existing links work fine?

I want to rename a custom doctype, it is linked to another doctype so will the links still work?
what does this “Merge with Existing” checkbox do?

You can also merge documents by renaming them. For example, if you have a customer named Steve and a duplicate named Steve1, you can go to either of them, click on Menu > Rename and tick the ‘Merge with existing’ checkbox. This will merge all the linked documents of both documents.