Edit in JSFiddle

(function(window, jQuery) {
  'use strict';
  
  var points = [
    { 'name' : '大洗 まいわい市場', 'point' : { 'lon' : 140.569693, 'lat' : 36.309830 } },
    { 'name' : '肴屋本店', 'point' : { 'lon' : 140.574143, 'lat' : 36.315018 } },
    { 'name' : '磯前神社', 'point' : { 'lon' : 140.587425, 'lat' : 36.315858 } },
    { 'name' : '大洗駅', 'point' : { 'lon' : 140.562624, 'lat' : 36.315675 } }
  ];
  
  var OpenLayers = window.OpenLayers;
  
  var projection4326 = new OpenLayers.Projection('EPSG:4326');
  var projection900913 = new OpenLayers.Projection('EPSG:900913');
  
  var labelStyleMap = new OpenLayers.StyleMap({'default':{
                    strokeColor: "#00FF00",
                    strokeOpacity: 1,
                    strokeWidth: 3,
                    fillColor: "#FF5500",
                    fillOpacity: 0.5,
                    pointRadius: 6,
                    pointerEvents: "visiblePainted",
                    label : "name: ${name}",
                    
                    fontColor: "red",
                    fontSize: "12px",
                    fontFamily: "Courier New, monospace",
                    fontWeight: "bold",
                    labelAlign: "lt",
                    labelXOffset: "0",
                    labelYOffset: "-5",
                    labelOutlineColor: "white",
                    labelOutlineWidth: 3
                }});
  var nonLabelStyleMap = new OpenLayers.StyleMap({'default':{
                    strokeColor: "#00FF00",
                    strokeOpacity: 1,
                    strokeWidth: 3,
                    fillColor: "#FF5500",
                    fillOpacity: 0.5,
                    pointRadius: 6,
                    pointerEvents: "visiblePainted",
                    
                    fontColor: "red",
                    fontSize: "12px",
                    fontFamily: "Courier New, monospace",
                    fontWeight: "bold",
                    labelAlign: "lt",
                    labelXOffset: "0",
                    labelYOffset: "-5",
                    labelOutlineColor: "white",
                    labelOutlineWidth: 3
                }});

  var map = new OpenLayers.Map({
    div : 'map_canvas',
    displayProjection : projection4326, 
    projection : projection900913,
  });
  
  var osmLayer = new OpenLayers.Layer.XYZ('OSM',
  	[
      '//a.tile.openstreetmap.org/${z}/${x}/${y}.png',
      '//b.tile.openstreetmap.org/${z}/${x}/${y}.png',
      '//c.tile.openstreetmap.org/${z}/${x}/${y}.png'
    ],
    {
      numZoomLevels:6,
      zoomOffset : 14,
      maxResolution: 9.554628533935547
    }
  );
  var markerLayer = new OpenLayers.Layer.Vector('marker', {
    styleMap : labelStyleMap
  });
  map.addLayers([osmLayer, markerLayer]);
  
  var centerPoint = new OpenLayers.LonLat(140.5748486, 36.3134009)
    .transform(projection4326, projection900913);
  map.setCenter(centerPoint, 14);

  for (var i = 0, len = points.length; i < len; ++i) {
    var name = points[i].name;
    var lonLat = points[i].point;
    
    var vectorPoint = new OpenLayers.Geometry.Point(lonLat.lon, lonLat.lat);
    vectorPoint.transform(projection4326, projection900913);
    var vector = new OpenLayers.Feature.Vector(vectorPoint);
    vector.attributes = {
      name : name
    };
    markerLayer.addFeatures([vector]);
  }

  // Change Label Visibility
  jQuery('#label_visible').on('change', function() {
    if (this.checked) {
      markerLayer.styleMap = labelStyleMap;
    }
    else {
      markerLayer.styleMap = nonLabelStyleMap;
    }
    markerLayer.redraw();
  });

})(window, window.jQuery);

<p>
  <label><input id="label_visible" type="checkbox" checked />show label</label>
</p>
<div id="map_canvas"></div>

#map_canvas {
  height: 350px;
  width:  350px;
}