If you replace div> then you will miss any opening tags that have attributes. E.g. <div class=baz> or <div id=foobar>.

In Vim I would do

    :%s@\(</\?\)div@\1p@g

It’s a little bit convoluted but it replaces the tag names in both opening and closing tags and does not replace it anywhere else.

I believe replacing `<div`\'<p' and `/div`\'/p' are preferred so you can retain any tag properties (class, id, style, etc), but it could still leave behind any tags with superfluous spaces.