(I cannot find much use in the renaming. It’s on your system, and you and your dog will know about the new biller’s name.)
Actual hyperlinks assigned to textportions can only be edited either by interaction or by user code (“macro”). You wouldn’t get the problem at all if you used the HYPERLINK function for the purpose, and probably it’s easy to change the design of your Calc sheet a bit to implement this solution. Renaming a folder would then only need mirroring in one single cell of one sheet in a Calc document.
I expressly do not advise, but if you decide to go the Macro-Do, you may check this contribution to a better structured forum, to get hints about how it might be done.
(Editing:) Really sorry. I must have miscalculated the implications of words used due to my poor English. Bad joke? No disrespect intended! I now also see that my answer above may not have met the question to its point.
Next attempt:
Sheet names of an open document are internal to Calc. Thus the software can update formulae - and it does.
Folder names are external to Calc and managed by the Operating System. Calc may be sleeping when a name is changed, and will also otherwise not be informed about the changes. With other words: There is no way for Calc to identify a storage location independent of its name which would be necessary to update folder names in formulae or hyperlinks on its own responsibility.