How to get a command block to say the name of a named mob

I'm making a horse racing track and I want the game to say "[name of horse] has finished the race!" when a horse crosses the finish line. I can get it to say the name of every horse in the area, but not just the one that activates the block.

If you're activating the command block with a pressure plate you could use the @e selector combined with sort=nearest and limit=1 like this:

/tellraw @a ["",{"selector":"@e[sort=nearest,limit=1]"},
{"text":" has finished the race!"}]

If players are riding the horses you could also add type=horse in the selector:

/tellraw @a ["",{"selector":"@e[sort=nearest,limit=1,type=horse]"},
{"text":" has finished the race!"}]