By which of the following names the District of Cuttack is also known?

Answer: Option D

The question is asking: What other names does the Cuttack district have?

Let's look at the options:
Option A: Silver City - Cuttack is indeed famous for its silver filigree work, so it's often called Silver City.
Option B: Royal City - While Cuttack has a rich history, it's not commonly known as Royal City.
Option C: Millennium City - Cuttack is also referred to as Millennium City due to its long and historic existence.
Option D: Both (A) and (C) - Since Cuttack is known as both Silver City and Millennium City, this is the correct answer.

Therefore, the correct answer is Option D: Both (A) and (C).