Most of the time there is a direction it came from, altitude and speed, so this allows you to know, from previous intel, which airport it took off from, and thus you know, from intel, what operates out there and thus what it is. Then you can either use a manned intercept or a missile to take it out if needed, or just keep it under observation until it crosses some imaginary boundary and becomes a target.
No major computer that can ID it, just a radar and commercial transponder to disambiguate commercial traffic, which should not be in a contested airspace at all, so you either have an armed escort making sure the errant commercial follows you to a designated landing spot, or it is warned off by comms on the international common frequency, and if it does not leave it becomes a target.
Standard ATC in that case is "Flight 7777, you are entering contested airspace, please turn to heading 270 and withdraw", which is invariably followed with the answer" Flight 7777, turning around". If no reply there will be 2 fully armed interceptors flying 10m from his cockpit within 5 minutes. At night they will be on full afterburner and full speed brake, so he will see the massive flame if the radio is off. Ignore for 2 minutes one will be upside down on top of the cockpit looking in to see the pilot, and after another 5 minutes of no reply and no visible reaction from the cockpit it will be escalated and somebody will give the final disposition order.
If it is not commercial it will have the 2 interceptors, and they will enquire what is the other doing in this airspace, and if there is any problem then it is going to be handled by the other 3 standoff aircraft flying 10 000feet above and behind.
Radar control enables you to see it take off, climb to altitude and then scramble 3 interceptors. They take off ( hot standby) and climb out at max power to fl600, dropping tanks as they go empty, then they are vectored onto the target vector. they then dive at max safe velocity till within missile range, and then either fire locked on heat seeker missiles at the unsuspecting target, or blow holes in it at close range with a 20mm cannon, then whip past at full speed and try to avoid hitting the ground. Then return to base and reload, and put the new paint silhouette on the side of the cockpit. Other guy knew nothing till bullets hit him, or a missile ran up the rear and detonated. If lucky he pulled the handle and was able to eject, or dug a hole with the plane.