I just installed Centos v7 64 bit with MATE as the desktop manager. I want to make changes to the login screen.

1) I'd like to go have a blank log-on name field displayed instead of a name and password field. I haven't found any help online. Can someone help?

2) I would like to change the background to a solid color. I have already changed the user's desktop screen to that, but I'm stumped for the log-on screen.

Hope you can help.

just to get some terms straight, mate is the desktop environment.
the bit you want to change is the responsibility of the display manager.
you have to find out which one CentOS or MATE uses.
then you read up on its documentation, and can surely achieve what you want.
i suggest you start with the background color; it's trivial and 100% possible on any display manager's greeter.

That's hardly helpful. I wouldn't ask if I knew what to look for.

For those who want to know, the image files are in /usr/share/backgrounds. Look in the default.xml file for filenames (day, morning, night) to change. There are jpeg files. Note there is a default.png file as well. You will likely need to use Inkscape to create a new default.png file that is 1920x1200 pixels in size, and then use the command-line convert command to create a jpg file from the png file. I suggest you save the originals in case things go wrong.

If someone has a less brute-force way, please contribute.

I don't have CentOS running right now, but try this: Open the control center and look for something relating to configuring the display manager or login dialog.

What It Does(Full Details) "/etc/nologin.txt" in any Linux Flavour

why not just launch "system-config-editor"

the "Swiss-army-knife" of gnome based tools

and edit the login background by changing the background that is used