Good news: custom page URLs no longer include /p/. Your custom pages now live right at the root of your site — for example, yourdomain.com/name-of-page.
If you shared a link in the old format (yourdomain.com/p/name-of-page), don't worry — those links automatically redirect to the new address, so nothing breaks.
Want a different address entirely? You can change the page's slug in its settings, or create a Shortlink that forwards any URL you say on your show to the page: in your dashboard, go to Settings → Shortlinks and click New Shortlink (available on the Pro plan and above).