Maybe a bit of a primer on how a NAS works. Basically, the NAS sits in the network and offers a protocol to other networked devices to attach to it. The format of the hardware is invisible to the network, as that is handled by the NAS itself. Network users who want to use the storage use the protocol from the NAS to send/receive data and have no insight into the format of the drive or where it is stored on the hardware. It's almost like a wall with a window in it. Behind the wall is a storage system that says, "Ask for something in this form and I'll get it for you" and "Give me something in this form and I'll store it for you." Where and how that storage is done is not visible to the user.
So what is key is that the drive be formatted in a format that the TP-Link needs and can use. That's key for the storage to be available. However, TM wants more, normally, to be able to use the drive if you connect it directly. But if you have a NAS and point TM to it, TM knows that it cannot proceed "normally" as it would with a direct drive, so it switches to a format called sparsebundle that can use ANY format drive. That way the data from TM can be stored on formats that normally TM would not be able to use directly.
So, going back to your most recent post, you let TM do a backup to the drive directly. That means the drive must be in a format usable to TM, which is normally MacOS Extended Journaled. I don't know if TP-Link can use that format, but for now let's assume it can. So you detach from the Mac and attach to TP-Link directly. But you cannot see the drive name. And that's correct, you cannot see behind that wall, even if you KNOW the name. The new address for that drive is whatever TP-Link assigns, not what you named it. TM shows the name in its list because it used the drive at one time and remembers it, even though it cannot now see that name because TP-Link is hiding it. As far as the system is concerned, the only NAS drive is whatever name TP-Link assigns it, period.
Earlier (post #20) you said TP had indicated that the TP-Link you have cannot be used with TM. That's your answer and no amount of trying will get past that. The protocol that TP-Link is using is incompatible with TM, apparently.
So it's a waste of time and energy to try to do the impossible. And that conclusion leaves you with two options: 1) Use the drive as a NAS for other purposes, assuming you need a NAS, and get a direct attached drive for TM and 2) Use the drive for TM by directly attaching it and go without a NAS drive. But it's useless to try to get TM to use that drive attached to the TP-Link. Not going to work.