Squarespace doesn't email the person who filled in your form. Pengon can. Under Settings, add your business name and turn on Visitor copies: people whose message gets through then get an email with every answer they gave. It's handy for bookings, RSVPs and orders.

It comes from your business name, as “Your business via Pengon”, and replies go straight to you.
Spam never gets a copy, and neither does anything Pengon isn't sure about.
Click Send me a test to see what it looks like first.

When there's no copy

So nobody can use your form to send emails to strangers, there's no copy when:

an answer contains a link, a web or email address, or a phone number outside the phone field;
the answers together are very long (more than about 1,500 characters);
the same address already got a copy from your site in the last 24 hours;
your site has already sent 100 copies today.

Plans

Visitor copies are part of the paid plans. During your free trial, you can set them up and send yourself a test. Your visitors start getting them once you subscribe.