Will the person I'm calling see my real phone number?

No — by default your real number is never shown.

The recipient sees a shared PuchiDen number, so you can place calls without exposing the SIM card or carrier line you actually own.

If you would rather have a specific number you control (a home line, a verified business number) appear on the other end, you can verify ownership of it once and add it as a caller ID in your settings.