Your VRChat account can be identified by a few different factors. It is important not to get these mixed up, as it can lead to confusion and make troubleshooting difficult.
Display Name: This is the name that is shown to other users in-app, viewable in the nameplate above your head and in menus. This can be changed by editing your profile on the VRChat website. If you're using a Steam/Oculus/Viveport account, your Display Name will match your name on the corresponding service, but with a four-character identifier at the end. When you change your name on the respective service, your Display Name will be updated to match the new one (plus the identifier) the next time you launch VRChat. To remove the identifier, see here for how to upgrade to a full VRChat account.
Username: This is the very first name you signed up with. Other users are not shown this directly in-app, but it can be viewed by other users who visit your profile page on the website. For Steam/Oculus/Viveport accounts, this will typically match a unique account identifier on the corresponding service, such as a SteamID. Your username cannot be changed.
User ID: This is a unique string of characters that identifies your account, generated upon creation. It is shown in the URL of your account on the website, and cannot be changed or customized.
When logging in to a VRChat account on the VRChat Application, website, or SDK, you need to enter your username or email address (not your display name), along with your password. If you're using a Steam/Oculus/Viveport account, or if your VRChat account is linked to one of those services, you can also access your account by signing in with the respective service in the VRChat Application only when launching the application via the same service.