I doubt this is true of California, but there are probably a number of states where Paul would lead Warren just off of higher name rec.
Yep. In this Quinnipiac national poll, her name recognition is only at 39%, while Paul's is in the 60s:
https://uselectionatlas.org/FORUM/index.php?topic=195277.0She's more well known than O'Malley or Klobuchar, but not as well known as the majority of the most often discussed GOP 2016 candidates. Hence, her performance in these polls is always going to be somewhat limited.