Get the PlayStation button mod for Tony hawk 1+2 (it works on 3+4) from nexus : https://www.nexusmods.com/tonyhawksproskater1and2/mods/51

Make a new folder in the thps 3+4 install at "base\Content\Paks\" called "~mods". Put the mod pak file into the newly created folder.
If you can't find the right folder, right click the game on steam and browse local files to find the install folder.

Load the game. When using controller, your prompts will always be PlayStation.

This should work on other platforms too but you'll need to change the file path to find the right folders.

Credit to geefour for making the original mod.

An EXAMPLE of how the file path should look. This may not be the same on your machine!

C:\Program Files (x86)\Steam\steamapps\common\THPS34\Base\Content\Paks\~mods