Try this script. You can save it as a script then run it in an action and assign a hot key such as F3. The scripts assumes that the path you want to rename is named "Work Path". It also assumes that the naming sequence is PS default's: "Path 1, Path 2...."
#target photoshop
var doc = activeDocument;
var works = true
try{
var curPath = doc.pathItems.getByName ('Work Path');
}
catch(e){
works = false;
alert('There is no path named "Work Path"');
}
if(works){
try{
var lastPath = doc.pathItems[doc.pathItems.length-2];
var pNum = lastPath.name.split(' ')[1];
curPath.name = 'Path ' + (Number(pNum) + 1);
}
catch(e){curPath.name = 'Path 1'};
curPath.deselect();
}