Step 1: Understand the question.
We must find which word is NOT formed with the prefix anu.
Step 2: Recall the prefix anu.
The prefix anu means following or after and is added before a root; we will split each word to check.
Step 3: Test anveshan.
$(A)$ anveshan is anu plus eshan, so it does use anu.
Step 4: Test anupam.
$(B)$ anupam is an plus upam, where an is a negative prefix meaning without, not anu. So this word does not use anu.
Step 5: Test the remaining words.
$(C)$ anuchar is anu plus char and $(D)$ anurag is anu plus rag, so both genuinely use anu.
Step 6: Conclude.
Only anupam stands apart with the prefix an, so it is the answer, option B.
\[ \boxed{\text{B. } \text{anupam}} \]