Q:

Hide SharePoint page title based on a Permission Group

I know that you can target audiences on web parts and such, but can you hide/show a page title depending on a site's permission group? 

A:

As far as I'm aware, you can't hide the title OOTB.  You'd have to add some sort of third party tool, or run some javascript. 
You could look into adding a script editor webpart in with code similar to the following:
<script language="javascript">
$( function() {
    // Get context for current page, set a permission level to evaluate, and set query to 
    // check if they have these base permissions
    var ctx = new SP.ClientContext.get_current();
    var web = ctx.get_web();
    var ob = new SP.BasePermissions();
    ob.set( SP.PermissionKind.manageWeb )
    var per = web.doesUserHavePermissions( ob )

    // Execute Query
    ctx.executeQueryAsync(
        function() { // On Success Query
           var titleField = document.getElementById( "DeltaPlaceHolderPageTitleInTitleArea" )
            if ( per.get_value() ) {
               titleField.style.display = "inherit"
            } else {
               titleField.style.display = "none"
            }
        },
        function( a, b ) { // On Failed query
        } );
} );
</script>

It's a self-executing function that checks for the user's current base permission level (like Edit, Contribute, Full Control, etc) then inside the success function (commented with // On Success Query) you put your script to change display.  This exact setup works on my publishing page on-prem 2013.  To change the permission type, you'll have to select a new Enumeration.  You can use this reference to get the different enumeration types.  To select your enumeration type, change SP.PermissionKind.manageWeb to SP.PermissionKind.anotherEnumerationwhere anotherEnumeration is from the reference above.