You cannot directly connect a PSP to the internet using a 3G dongle. The PlayStation Portable only supports Wi-Fi for internet connectivity and lacks built-in support for cellular data.
The PSP's hardware only includes a Wi-Fi (802.11b) radio. It has no USB host capabilities to communicate with a 3G dongle, nor does its operating system contain the drivers needed to initialize and manage a cellular modem.
Create a Wi-Fi network that your PSP can join:
Some compact travel routers (e.g., older models from TP-Link, ASUS, or HooToo) feature a USB port specifically designed to accept certain 3G/4G USB modems. The router handles the dial-up connection and broadcasts Wi-Fi for the PSP.