It is certainly possible to use goat cheese in making cheesecakes, but as Andy wisely points out, you may not be happy with the results. It will taste nothing like a cream cheese cake.
I routinely substitute goat ricotta, chevre and other soft goat cheeses for cream cheese in cheesecakes, blintzs, and other desserts. They can be delicious in their own way, but it will not taste like a cream cheese based product. I have found I need to add a lot of something that adds flavor, such as a double dose of a good quality vanilla or almond extract, or cream.
Good luck with this experiment and I would be interested to hear how it turns out. I am always looking for a good chocolate goat cheese dessert