It’s generally not feasible to hide usernames entirely; each user is required to have a unique username, but many users may have the same full name.
To prioritize using full names in mention suggestions, you’d need a custom plugin. I don’t think anyone’s built one that does that yet.
For hiding usernames on posts, some CSS should be able to handle it…
.topic-body .topic-meta-data .username {
display: none;
}
Note that this CSS change could cause some abuse problems. If usernames are hidden, I could change my full name and avatar to match someone else’s, and without a username it becomes much harder to see the difference.