Hi,
Firstly I'm including CHELSEA, because you requested it to be stated in our bid.
I'm skilled in PHP, JavaScript, HTML, CSS, so I can solve this for you.
Here's how I would do it:
1) Create a text file with 100 names, every name a new line, so it would be easy in a future to view, edit or add names to it
2) A PHP script that reads and processes those names, and every time that it's called returns one random name from the text file.
3) A small JavaScript (jQuery preferred) code that communicates with the php script, and picks a random number from 1 to 9.
I have a question though. I can see that on the site you linked this same script refreshes itself in like every 5 seconds. It gives a new name and a new random number. Do you need this functionality too, or you would be fine without this one? Btw. it's not a problem to have it work this way, I'm just asking to clarify.
Thank you for reading my kinda long proposal.
P.S: depending on how quick you need this, I think I would be able to finish this for you under my original bid of 2 days.