With the web interface and the left-side uncontrolled-streaming-list of chat sessions (NOTE : OpenAI, please add some organisational tools!), you can have a session become relevant again at the top of your list. Use the “ooo” more button on your session heading/label, then “Rename” option. You can add a simple space at the end or whatever you want, and once accepted the session jumps to the top of the list. 
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This is an anti-pattern.
I have a long list of sessions with unhelpful autogenerated names. Now that my list is getting difficult to search I would like to give them all better short clear concise names. However if I do that I would mess up the “importance” of them by bringing each renamed session to the top.
I want to rename them without disrupting the most-recently-used order.
Good point Peter. This probably won’t help much, but I guess you would have to go through all of them in order from the bottom to the top. This means, even chats you didn’t want to rename, but might need to force the change (ie. add a space so it does change). Then when you get to the top listing (by PURPOSELY renaming it first before starting all this, in some identifying way, eg. CAPS), then you’re done and the list should be back in sequence order with new names… but, what a way to manage files/items 
As it stands, I won’t rename a conversation because it messes up the chronological order and just makes it confusing to be back at the top. It feels more like a bug than a feature, after all no one has said anything new in the so-called “conversation”.
I really wish this was not the case, or at least optional. Please add a setting, it shouldn’t be too hard to implement. (+1 for adding organisational tools ).
For now, it seems like I need to write a userscript (with ChatGPT) to fix the order of the shitload of conversations I have with ChatGPT, all having almost the same generic conversation name since i mostly write userscripts with ChatGPT