Step 1:
Ancient Ujjain was popularly known as:
\[
\boxed{\text{Avantikāpurī}}
\]
Hence, Assertion (A) is correct.
Step 2:
Ujjain is situated on the banks of river Kshipra and is traditionally associated with King Vikramaditya.
Thus, Reason (R) is also correct.
Step 3:
The rule of Vikramaditya does not explain why Ujjain was called Avantikāpurī.
Step 4:
Therefore:
\[
\boxed{\text{Both (A) and (R) are correct but (R) is not the correct explanation of (A)}}
\]
Hence, the correct answer is:
\[
\boxed{\text{(2)}}
\]