I have read the wiki and found where it talked about how to handle named chests, however, I can't find where or how you name it.
If I have the Only Named: ON the items don't get added to the list, I have named the chest via the anvil but with no luck.
So how do you apply a name to a chest?

Still not sure about the original issue, but I've added the ability to rename stuff client-side.

Hopefully the underlying issue you had is solved by the internal changes between then and now.

I'm struggling to reproduce this but it sounds like a bug. Chest Tracker (currently) doesn't do the renaming, it just reads from the GUI title. What I can think of:

1. Are you using a modded chest or container? might have a custom GUI implementation that Chest Tracker isn't reading.
2. Make sure that other settings aren't blocking the chest (filtered out with 'Common Containers')

The chest is on a Paper Server.
And I changed the settings to what you had it on.

This is odd, I logged out of the server that I was playing and just now logged back in to test further, and now any chest that I open thinks it's named even when it was not named

The Testing is the edited name. The other 2 are normal.

Also, I deleted and replaced the original Memory Bank.
However, the name-only settings were on the 2nd (Current) Memory Bank.
(I was playing around with the settings)