The issue here is that you are using official firmware
Official firmware blocks the use of installing games by placing the ISO or CSO into your PSP's directory. The only way to fix that is through the use of custom firmware
So which do I install then?
As ythe version of your PSP is 6.20, I would recommend you install the 6.20 ME-1.9. That is the most up-to-date version of the CFW produced by ME. Please note, make sure to read the instructions very carefully, and see if your model is supported. If not, this could potentially lead to your PSP bricking, rendering it useless.
Link to their website
But wait...
If you can, however, I would strongly recomend that you instal the official 6.60 firmware, then installing the 6.60 ME custom firmware. This way, you can get the most up-do-date version of ME that supports the features introduced to 6.60
Link to their website