Automator and Variables in AppleScript

It would help to describe exactly what you have tried so far in order for anyone to determine what you mean by "can't seem to", but it is up to you to define whatever variable(s) you want to use. To replace the "Test Notification" text, your script would look something like:

on run {input, parameters}
  tell application "Finder" to set theName to name of first item of input
  tell application "Messages"
    set iMessageService to first service whose service type is iMessage
    set iMessageBuddy to buddy "whoever" of iMessageService
    send theName to iMessageBuddy
  end tell
end run

The input parameter of the Run AppleScript action will contain the items sent from the previous action, so you can use something like first item of input or loop though all the items, for example

    repeat with anItem in input
      # tell application "Finder" to set fileName to name of anItem
    end repeat

Normally you would need to add an action to get file names, but since you are using an AppleScript action you can just use the Finder to get them.

You can use regular string concatenation, for example:

send theName & " is ready to edit" to iMessageBuddy

Replace that first tell statement with:

tell application "Finder" to set {theName, extension} to {name, name extension} of first item of input
if extension is not "" then set theName to text 1 thru -((count extension) + 2) of theName