I cannot find option for changing character portrait in GBC. IS there any other way to change it?

I would imagine the only way is some kind of code manipulation in the save file. It's likely not in GBC because POR is the only game that used them, thus would not be worth the time to code. Since you're already using GBC, you might as well just transfer all the gear off, make a new character with the portrait you want, then level it back up with the GBC editor.