I'm aware of Benford's law that covers the distribution of leading digits:
Benford's law, also called the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data.
However, I'm wondering if there's a name for the distribution of digits throughout numbers. For example, the distribution of digits for the number
0, 2, 4, 5, 6, 7, 8 and 9: 7% each
What is the distribution of digits, throughout a number called, and where can I learn more about it?