Yes you can.  You have the option to customize the confirmation, thank you, error etc. HTML pages and emails.

You can make these look like anything that you like. You can even create different forms for different sites so that all the corresponding pages and emails are of the same look and feel.

There are two places that control different parts of the subscription process:

Under Lists > Email Confirmation Sets, you can control the email sent to the user requesting them to confirm their subscription.

Under Integration > Forms, you can edit a form and click on "Form Completion Options" at the bottom to open a group of options which will allow you to control the messages that appear, such as the Successful, Confirmed, and Error messages.