var obj = {
  name: "student",
  contact: {
     phone: "22222",
     fax: "33333",
     ...
  },
  ...
}

<input type="text" name="name" />
<input type="text" name="contact_phone" />
<input type="text" name="contact_fax" />
...

$("#formID").find("input").each(function(index) {
    fieldName = $(this).attr("name");
    var namePart = fieldName.split("_");
    //I want something like this: console.log(obj.namePart[0].namePart[1])
});

obj[namePart[0]][namePart[1]]

$('#formID').find("input").each(function(index) {
    fieldName = $(this).attr("name");
    var namePart;
    if(fieldName.indexOf('_') > -1){
        namePart = fieldName.split("_");
        console.log(obj[namePart[0]][namePart[1]])
    }
    else{
        namePart = fieldName;
        console.log(obj[namePart])
    }

});