For renaming you can write a one-time-use code afterwards.
I assume you will move from /content/dam/old_name to /content/dam/new_name. So you can write a job that will run during the night and that scans all your Pages/Components, CFs and XFs and modifies the properties values when it encounters smth that starts with /content/dam/old_name. You can log all you changes somewhere for future verification. In case you know the components where you use references to these assets, you can target only those on lookup. You can even target only specific properties if you know them.
What I want to point out, is that there are options. Depends on how much time you have and level of effort available to put into this, if none of the ootb ways work.