Can you create duplicate character names in Planetside 2?

No.
Every single character of any user of any faction on any server has a unique name.
Although first-hand evidence is hard to come by in the form of a FAQ topic or something similar, there are enough leads:

  • It can be inferred from randomly found screenshots of character screens;

    Randomly found screenshot #3749 - no affiliation

  • Or from visiting fora threads like this one.

This has probably played a major role in how in Planetside 2 "every username is already taken".

Advice: change the capitalization of one of the characters, since it will register as a unique username (unless taken, of course).