jQuery UI input autocomplete without anonymous function

I managed to get jQuery UI autocomplete to work. However since I use it in many input fields I wanted to make it more generic so I don't have to replicate it. So instead of the following code:

$(function() {
    var cache = {};
    $("#searchGuyInput").autocomplete({
        minLength: 2,
        source: function(request, response) {
            // Getting a JSON array to populate the list
            var term = request.term;
            if (term in cache) {
                response(cache[ term ]);
                return;
            }

            $.getJSON("c_select_guy.php", {request: term}, function(data, status, xhr) {
                cache[ term ] = data;
                response(data);
            });
        },
        select: function(event, ui) {
            // What happens once I have selected a name from the list
            if (ui.item){
                createInputField(ui.item.Name + " " + ui.item.Surname,ui.item.guyID);
            }
        }
    })
    .data( "ui-autocomplete" )._renderItem = function( ul, item ) {
        // Here I can format the JSON array to display the rows in the list
        return formatted;
    };

    function createInputField(message, guyID) {
        // creates a new div for the selected element
    };    
});

I tried to use:

function autocomp(inputID) {  //CHANGED
    var cache = {};
    $(inputID).autocomplete({ //CHANGED
        minLength: 2,
        source: function(request, response) {
            // Getting a JSON array to populate the list
            var term = request.term;
            if (term in cache) {
                response(cache[ term ]);
                return;
            }

            $.getJSON("c_select_guy.php", {request: term}, function(data, status, xhr) {
                cache[ term ] = data;
                response(data);
            });
        },
        select: function(event, ui) {
            // What happens once I have selected a name from the list
            if (ui.item){
                createInputField(ui.item.Name + " " + ui.item.Surname,ui.item.guyID);
            }
        }
    })
    .data( "ui-autocomplete" )._renderItem = function( ul, item ) {
        // Here I can format the JSON array to display the rows in the list
        return formatted;
    };

    function createInputField(message, guyID) {
        // creates a new div for the selected element
    };    
}

autocomp("#searchGuyInput"); //CHANGED

I highlighted the 3 changes with //CHANGED comments for you.

However now even though the autocomplete returns me a nice populated list of elements, when I select from the elements in the autocomplete the ui.item variable in the select function is undefined and it doesn't work anymore!

What am I understanding wrong?

I thought the $(function()); was just a way of defining an anonymous function in javascript and hence if I made it named I could call it multiple times for different input fields.