Final answer:
The letter name and octave designation for the piano key with the dot depend on its position on the keyboard.
Step-by-step explanation:
The piano key with the dot is known as a sharp, represented by the '#' symbol. The octave designation for this key depends on its position on the piano. Each octave contains 12 keys, including both white and black keys. To identify the specific octave, the scientific pitch notation system is commonly used, which assigns a number to each octave. Middle C is usually designated as C4, with each higher octave incrementing the number by one. Therefore, the octave designation for the piano key with the dot would depend on its position on the keyboard.