Why do you think Pucci has a Stand that (seemingly) has such an independent personality, to the point that Pucci feels the need to give Whitesnake direct orders like "Search" or "Give me a disc"? Or is that just how Whitesnake, similar to Echoes ACT3 or Spice Girl, developed to better protect Pucci's identity as an autonomous agent (with a larger role in the wider scheme of things than either of those aforementioned Stand examples)?
Beyond the fact that it adds interest to the story? Part of it might be Araki’s way of showing that Pucci himself has very little conscience. Whitesnake’s sort of neutral and objective, sometimes it almost seems like he’s questioning why Pucci’s asking him to do things. Whitesnake shares Pucci’s ruthlessness and aims but he’s also shown to be reflective, even philosophical, during times when Pucci just wants him to get stuff done.
It’s almost like it’s a manifestation of how much self-justification goes into Pucci believing that what he’s doing is Good instead of evil. The Pucci we meet in SO fully believes that he’s righteous … but maybe Whitesnake’s independence/objectivity developed as a manifestation of how Pucci needed at some point to compartmentalize and willfully ignore the wrong he was doing until it became second nature. Pucci got his Stand right after Perla’s death.
I don’t know that Araki intended all that but like I said, that’s how it winds up feeling.