We can add the custom jQuery code in the default edit form like the picture below. And edit the default edit form, add the script web part and add the custom jQuery code in the script web part.

There is a demo.
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.3/jquery.min.js" type="text/javascript"></script>
<script type="text/javascript">
$(function () {
$("#ctl00_ctl40_g_208827b4_894c_4842_bbdf_f311bae2ed4a_ctl00_ctl02_ctl00_toolBarTbl_RightRptControls_ctl00_ctl00_diidIOSaveItem").click(function () {
var value = $("select[title='look1 Required Field']").find("option:selected").text();
alert(value);
});
});
</script>
The result as below, when I click the “check in”, it will alert the selected value in lookup column.

There is a similar post:
https://social.msdn.microsoft.com/Forums/office/en-US/529ee28f-80bf-44a6-9cb4-392e74213076/how-to-get-value-from-lookup-field-on-onchange-event?forum=sharepointdevelopmentprevious
To change the name of the file as the “Name and lookup column value”, you could refer to the demo below.
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.3/jquery.min.js" type="text/javascript"></script>
<script type="text/javascript">
$(function () {
var look1 = $("select[title='look1 Required Field']").find("option:selected").val();
var name = $("input[title='Name Required Field']").val();
$("input[title='Name Required Field']").val(name+" "+look1);
$("select[title='look1 Required Field']").change(function(){
$("input[title='Name Required Field']").val(name+" "+$(this).find("option:selected").val());
});
});
</script>
The result as below:

