For EVE Accounts that were created through buying EVE Online via Steam, the launcher should automatically log the user into the EVE account that is associated with their STEAM account. This account should carry your Steam display name within the account list in the launcher. If the launcher displays any entry fields asking for log in credentials, or only shows other pinned EVE accounts, the Steam authentication could not be completed.
The most common reasons for the authentication process to fail are Steam having been started in offline mode or the communication attempts of the launcher being blocked by a security software or firewall. If the game has just been bought on Steam, it can be worth trying to close the launcher and restarting the game through Steam as well, as it may take a few minutes after purchase until the account creation and linking is complete.