Managing your avatar in WordPress

The default for managing your avatar in WordPress is using a gravatar. This means you need to sign up at gravatar.com and add some avatar images to your new account. The e-mail address you at gravatar.com and for your WordPress sites will link the avatar image from gravatar.com to your sites.

The process is a bit cumbersome for users that just need to make some posts on occasion or need to be a part of a site. So plugins are created to fix this cap.

Here are two:

https://wordpress.org/plugins/avatar-manager/

https://wordpress.org/plugins/wp-user-avatar/

It is being worked on adding an avatar feature into WordPress so the user can upload and use their own image without having to sign up at gravatar.com.
https://core.trac.wordpress.org/ticket/16020

Here is a screenshot from how Avatar Manager adds managing Avatars to the your profile screen.

Displaying multiple avatars selecting which one to have active could be a good way of handling this.