It's like a crowbar with a screwdriver handle.
I have found one called KM-569-A, but I need one for a job, and I have no idea what its called!
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So, What is this called?
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Sign up to join this communitySimilar tools are also available for automotive trim removal. They are often called "automotive trim removal tool" (go figure, eh...)
That is a nail-puller or tack-puller (more commonly tack-puller with the screwdriver-type handle). You can get similar function from a "cats-paw"
The tool you want is called a "tack puller". A search in Google will show a plethora of styles.