Inkan registration for second name

I'm moving to Japan in a few months and I'm planning to buy my first hanko online. I have a japanese surname with two given english names and I was wondering if I could omit my second name when I register my inkan.

For better understanding, let's say my full name is TANAKA, JOHN PAUL LOPEZ. Can I just use 田中ジョン on my inkan? Or will they have to refer to my whole name registered on my passport and zairyu card (田中ジョンポールロペス)? Checked the local city hall website for reference, but they didn't have any information on second names for foreigners.