By default, the platform does not have this option to change the Message icon on your site. You can use the following CSS code.
Please follow the steps below:
1. Go to WordPress Dashboard > Appearance
2. Customize
2. Additional CSS
3. Append the following:
.messages-wrap i.bb-icon-inbox:before { content: 'ee62'; }
4. Click on Published to save the changes.
Font Cheatsheet
You may choose the code icons from the link below.