IDENT is a special transponder function that only gets used at ATC's request. ATC will ask for it when they're having trouble picking your 'blip' out of all the traffic on their radar screen, or if you're VFR (which means you're squawking 1200, if you even bothered to turn the transponder on), not on a flight plan, and they need you to squawk a specific code for them so they can keep track of you more easily. This might happen if you're requesting to enter controlled airspace at your destination airfield, or you're picking up a flight plan (can be instrument or visual) after you're already airborne.
When ATC radar sweeps the airplane, its transponder normally replies with that 4-digit number in a 12-bit code (called a secondary return). When you press the IDENT button, it changes to a 13-bit code, and receipt of the extra bit makes your 'blip' on ATC's radar screen pulse momentarily (computer geeks would call this "throbbing").
So all IDENT does is make your blip stand out from all the others that at that moment are on ATC's radar screen.
Can you use a false transponder code? Sure, most transponders have four thumbwheels on the control face that the crew manually sets the squawk code in. They can set it to anything they want from 0000 to 9999. Which might be conflated with a false identity but to IDENT is something altogether different.
I wasn’t clear about the relationship.
If ATC is giving you a specific transponder code to use and want to see your blip on the screen flash, they will tell you something like, “Squawk 5678 and IDENT.” So you change the transponder code to 5678 (which will take some seconds, during which you’re traveling 150 feet a second) and then press the IDENT button. So the IDENT is both a time saver for ATC and a safety feature.