With regard to your wife's computer, during setup you created a Microsoft Account linked Windows 10 user account, using your own e-mail address, and which will show whatever name you have associated with your Microsoft Account.

If you want your wife to be the sole account on the machine then you will need to set her account up, whether that's a local account or a Microsoft Account linked account using the e-mail address associated with her Microsoft account, as an administrator and then use that account to remove your own. If you set it up as a local account whatever you name you give the account will show up on the lock screen. If it's linked to a Microsoft Account, the name you have in the Your Info section of the Microsoft Account is used on the lock screen.

With regard to your daughter's computer, since hers is currently an administrator account (and must be, if it's the only account), you could use it to set up another account with admin privileges for yourself. Then after you have those privileges you can convert your daughter's account to a standard account, removing administrative privileges, if that's what you want to do. That or do a completely clean reinstall of Windows 10, set your own account up first, then set up a standard account for your daughter.

 

Thanks. But regarding the first thing, I don't think my wife has a Microsoft account. Even if she did she would never remember her info.

 

You have created a thread and placed it in the Windows XP section of the Forum. Will a Nice Mod please MOVE this thread to the Windows 10 section?
If your wife has associated her Email account as a Microsoft account, when it asks for your Email address it fills in the rest with your name.
If you want to be the administrator on your daughters computer, you are going to have to login as her with her password, then create an Administrator User account. Sign out as her and login as the New Administrator. Now you can demote her account to a Standard User, and you will be the only administrator.

 

Moved.

 

A first time user online of a Windows 10 Home account, will not get the option to create an Offline (Local) account, only in Pro.
If you disconnect from the Internet, Home will give you option to create an Offline account.