If you want to make your Rust server private and only allow certain players to join without having to remember a password, a whitelist plugin is meant for you. Rust currently does not have a built in whitelisting feature, so you can use an Oxide plugin to get the job done.
1. Enable Oxide on your server.
2. Add the plugin
Whitelist.cs and restart the server.
3. Join the game or via RCON run
oxide.grant user STEAMID whitelist.allow
*Note: Replace STEAMID with the player's Steam ID.
Your server will now be whitelisted.