セルフレジって英語でなんて言うの？

Supermarkets may have either manned checkouts - which means a cashier will receive your payment, or self service checkouts where you scan goods and make payment yourself.
EX. "It is so much more convenient and quicker to use the self service checkout."

Self checkout = when you check out your purchases yourself in the supermarket.
Self service = when you serve yourself in a store or food establishment.

Self service means that you do it by yourself without anyone else helping you.
A checkout is a till in a supermarket where you pay for your goods/items
So you would say 'Self checkout' or 'Self service checkout'

A "self-service checkout" or a "self checkout" is a service used when a customer pays for their items without the help of a cashier.
E.g.
-Walmart is introducing a new self checkout system that will be implemented in May next year.
-Self-service checkout is very convenient.