If you are absolutely sure the defect is in the main IC, the picture shows a chip-on-board (COB) that has no features that identify its model.
You can draw the circuit and try to find a similar commercial part number.
Cyrustek is a common DMM IC manufacturer and has a model named
ESS1960 which is similar in features as the whole multimeter. You need to look at its datasheet compare with the circuit of your DMM.
After that you need to purchase the IC - however, finding it for sale might be difficult.
Since the entire multimeter is not very expensive, the repair of your unit is not worth the effort if the IC is indeed damaged. If the damage is in another device, then it may be worth to repair.