You have to close the file object newFile, otherwise the buffer that you are really writing to when you call newFile.write() might not get flushed to the actual file on disk. That is, add this line at the end:
newFile.close()
Python has a nice construct for dealing with this "setting up and tearing down" logic, known as context managers, used by the with statement. Using this, you can change your code to
Text = "Hello"
newFileName = input("What would you like to name this file? ")
with open(newFileName, 'w') as newFile:
newFile.write(Text)
print("Saved as ", newFileName, "!")
When the with block is done, the file is automatically closed, even if some error happens in the middle.