php logic issue: uploading file and changing name

I am new to php and trying to figure out how to perform the following process: Using the below code to upload images submitted by users, I want to change the name of the file based on user session data, and if the newly named file already exists, then replace it with the current upload.

At the point where the following snippet is taken from is where I think this process should happen. However, instead of checking if the file exists, I want to just accept the file, rename it to something like ($_GET['session_name'] . "-avatar" . $extension), and if that file already exists in the uploads folder, then replace it with the current uploaded image. And finally, the file's extension shouldn't be a factor in determining a files existence, this way only one file per user will exist no matter the type of file.

// edit following to rename file, and if exists already, replace with current
if (file_exists("uploads/" . $_FILES["file"]["name"]))
  {
  echo $_FILES["file"]["name"] . " already exists. ";
  }
else
  {
  move_uploaded_file($_FILES["file"]["tmp_name"],
  "uploads/" . $_FILES["file"]["name"]);
  echo "Stored in: " . "uploads/" . $_FILES["file"]["name"];
  }

Complete code below (source):

<?php
$allowedExts = array("jpg", "jpeg", "gif", "png");
$extension = end(explode(".", $_FILES["file"]["name"]));
if ((($_FILES["file"]["type"] == "image/gif")
|| ($_FILES["file"]["type"] == "image/jpeg")
|| ($_FILES["file"]["type"] == "image/png")
|| ($_FILES["file"]["type"] == "image/pjpeg"))
&& ($_FILES["file"]["size"] < 20000)
&& in_array($extension, $allowedExts))
  {
  if ($_FILES["file"]["error"] > 0)
    {
    echo "Return Code: " . $_FILES["file"]["error"] . "<br>";
    }
  else
    {
    echo "Upload: " . $_FILES["file"]["name"] . "<br>";
    echo "Type: " . $_FILES["file"]["type"] . "<br>";
    echo "Size: " . ($_FILES["file"]["size"] / 1024) . " kB<br>";
    echo "Temp file: " . $_FILES["file"]["tmp_name"] . "<br>";

    if (file_exists("upload/" . $_FILES["file"]["name"]))
      {
      echo $_FILES["file"]["name"] . " already exists. ";
      }
    else
      {
      move_uploaded_file($_FILES["file"]["tmp_name"],
      "upload/" . $_FILES["file"]["name"]);
      echo "Stored in: " . "upload/" . $_FILES["file"]["name"];
      }
    }
  }
else
  {
  echo "Invalid file";
  }
?>