Incorrect Model Identifier and dont show Model Name

Actually, the model identifier is correct.

The model identifier for the 2.8GHz non retina 21.5" Late 2015 iMac is 16,2

16,1 sis for the 1.6GBz version.

Note that 16,2 is also the model identifier for the retina 4k 21.6" late 2015 imac

Why Apple does this isn't clear, but that's the way it is.

... but the performance speed made me very sad...

If this iMac came with the original 5400rpm, SATA 3G laptop-class hard drive that was standard then, that is the prime reason for the slowness. That is the #1 cause of "it's slow!" complaints here for 21.5-inch iMacs made between 2012 and 2019—regardless of processor or model identifier. The factory entry-level hard drives in 2011 21.5-inch iMacs were demonstrably 30-40% faster than those that came later. I've tested them.

👉🏻 However, this:

shows the computer already has a solid-state drive, likely retrofitted, so should be fast enough unless something else is at play. Even the slowest SSD option should transfer data at 6-8X what the original mech drives could. I think there is more to your "slows" that we have not yet seen.

You may want to post an Etrecheck report to help us see if something else is afoot:

https://etrecheck.com/index

The free version will do nicely for this purpose, although the app is worthy of our financial support.

With it we can see hard data about:

• drive performance
• software interference issues, and
• RAM usage.
• crashes

Hard data conquers guessing every time.

Etrecheck is the development of a long-serving and trusted contributor here expressly for displaying information in these forums to help us help you by remotely evaluating Mac issues. It will not reveal any personal or secure information.

Please see this excellent user tip on how to post long text reports like EtreCheck's into a forum response:

How to use the Add Text Feature When Post… - Apple Community 

As a general rule of thumb we recommend that users NEVER buy Macs from:

• Ebay
• Craigslist
• MarketPlace
• Local PC shop
• etc..

Why, frequently you have no idea what you are buying. The computer may be obsolete (as the 2015 that you bought is!) was not setup correctly per the directions in What to do before you sell, give away, or trade in your Mac. Also, you may simply be inheriting someone else's problems.

If you cannot afford to buy a new Mac, then the best place to go is to Apple's refurbished store. These devices are identical to new, have the same warranty as a new machine, are eligible for AppleCare and can save hundreds of $$$. In short there is no downside! In the US (I don't know where you are located) navigate to www.apple.com and scroll to the bottom of the page and find the Refurbished store. This is not available in all countries.

If you still cannot afford an Apple Refurbished then buy from a reputable reseller such as macsales.com.

It seems you have had the computer for awhile now so it's likely too late to return it. I would consider this a lesson learned on why you should not buy a Mac from Ebay.

Best of luck.

+1 Sadly if the return window is gone, then there is no recourse.

Please read my post above. There is no "problem". The model identifier is correct.