Firstly try cpu-z as mentioned above or you could open up powershell on your laptop and run the following command, Get-CimInstance CIM_Processor.
If you are still not satisfied with what you find, the sure shot way to actually determine the name of cpu would be to find the specification sheet of the exact model of your laptop. On a side note, just by searching for the model of your laptop, you are likely to come across asus's website where they list down all the different cpus, ram configs, storage specs etc. that have been used in variants of laptops under the same model.
In case you arent able to determine the cpu model of your laptop, as pinpointing the exact specs of an asus laptop can be tricky at times (by googling) - one of the reasons being that product specifications may differ from country to country; its best if you check with your local dealers for the specifications of the products available in your country.