where do you find registered device ID and what is that?
M7350 can only change the wireless name on it web management page.

I have no idea where to find it, only knowledge that my provider knew I used the tp-link router, instead of a regular mobile. That's why I want to change it.

It seems there is no way to change the device name.
I think it is not the device name but the mac address your provider recognize. From the mac address, we can know what manufacture a device belongs to.
Your provider will have the mac address of the router, cause the router need to send data to your provider.

I'm very curious about your case. Will you provider stop your service if you use the tp-link router?

Although I'm not an expert when it comes to this, I highly doubt the MAC address gave it away. Every physical device connected to the internet has a MAC address and there 281,474,976,710,656 addresses available. There isn't a list anywhere in the world that exposes which MAC address belongs to which (type of) device.

And to answer your question, yes they would. It's funny how support deals with this. They think that a mifi router will open up a steady stream of data or something. Obviously it's the number of devices that are connected to it. And also the type. I'll get back to that. But they think mifi routers will consume more bandwith than when you'd normally access the internet with the devices that I had connected to it. Three phones (1 Android, 2 iPhones), 1 iPad and occasionally 1 laptop. It consumes as much data as when you'd use your phone as a hotspot where others can connect to. But for various reasons I don't like that option and favor my mifi router.

About the type of devices... I came to the conclusion the Apple products demand much, much more on data then Android devices. Especially when those Android devices are put on battery saving, or individual settings are properly set to save bandwith. With Apple products this is simply not possible. It's also a shame that the TP-Link router doesn't tell Windows that it is is metered connection. Windows can work with metered connections, if it knows, and download/sync less data in the background.

But anyway, my provider was able to tell it was a TP-Link router and therefor I'd like to change the name it identifies itself with.

Here is an link for how to find the company a device belongs to: https://aruljohn.com/mac.pl
It may be not very accurate.

Very less network device will tell it is a metered connection automatically.M7350 has a data usage settings to limit the total data usage, you may need this.