I give her about 1/2 cup every morning. She never finishes it.

Mine don't drink much during the day. I see them have a couple of laps a few times but that's pretty much it until after they have their walk.

You can do a dehydration test.
Just lift the pups lip and press your finger against their gum and then let go. If it goes white and stays white for more than a second or two then it is a sign of dehydration.
If the gum goes pink again straight away she is fine.

Is there any reason why they don't always have access to fresh water?
I would make sure they always have access to water, even if it means you have to take them out more often.
Generally a dog needs at least one ounce of water for each pound of body weight per day but environmental factors, level of activity, and health condition can drive this need up much higher
Puppies are among the higher at risk for dehydration.

Is this the amount that is left down for her throughout the day?

Does she have any other places where she could be getting water?

Do you give her wet food, dry food or a mixture?