I have asked to keep polygon, name of the polygon and the corresponding icon in the places panel.
Can any suggest me how to do this in kml?
By default you only see the name label if your placemark has a Point geometry so for lines and polygons the name is not shown.
You can however create a MultiGeometry with both a Polygon and a Point (typically the center point or where you want to label to appear near). If you don't want the default yellow pushpin to appear just add a Style with an empty IconStyle href element to the Placemark.
<?xml version="1.0" encoding="utf-8"?>
<kml xmlns="http://www.opengis.net/kml/2.2">
<Placemark>
<name>polygon</name>
<Style>
<IconStyle>
<Icon/>
</IconStyle>
</Style>
<MultiGeometry>
<Point>
<coordinates>-122.4317195,37.801848</coordinates>
</Point>
<Polygon>
<outerBoundaryIs>
<LinearRing>
<coordinates>
-122.43193945401,37.801983684521
-122.431564131101,37.8020327731402
-122.431499536494,37.801715236748
-122.43187136387,37.8016634915437
-122.43193945401,37.801983684521
</coordinates>
</LinearRing>
</outerBoundaryIs>
</Polygon>
</MultiGeometry>
</Placemark>
</kml>
This multi-geometry method can be HIGHLY tedious if you have a couple hundred polygons (say, a grid/index) and you want to show their names.
My preference is to use something like QGIS/Arc, where I create a new vector file of polygon centroids (point file) that has the polygon attributes (including name/description). I save the new point file as a point KML and import into Google Earth. From their, I set a shared style for the point file, with the icon set to 0% opacity.
Example of Google Earth Polygons with Labels using above method