There's a few ways can customize how the chat widget appears on your storefront, but before we dive in just a reminder the chat widget should have been added to the store (see how in case it wasn't added yet).
You can also hide the chat icon and trigger the chat with a link or button, by following this guide.
Other than that, from Settings > Inboxes > Shopify chat widget > Branding, you can you customize the widget's:
-
avatar, colors and position (left or right)
-
the bubble type and the launcher title ("Chat with us")
-
z-index, vertical offset or how many pixels between the widget and the bottom of your page
