You could use a command like
Rename TO={modifieddate|D#yyyyMMdd}\*
but for your specific case you'll need a script like this:
// https://resource.dopus.com/t/how-to-retrieve-the-modification-date-of-a-selected-file-in-a-command-line/52498
function OnClick(clickData) {
var cmd = clickData.func.command;
var tab = clickData.func.sourcetab;
cmd.deselect = false;
if (!tab) return;
if (!tab.path) return;
if (!tab.selected_files.count) return;
cmd.SetDest(tab.path);
var cmdLine = 'Copy' +
' MOVE' +
' COPYFILETIMES=all' +
' CREATEFOLDER="{dlgstring|Enter folder name:|' + tab.selected_files(0).modify.Format('D#yyyyMMdd') + ' }"';
// DOpus.Output(cmdLine);
cmd.RunCommand(cmdLine);
}
XML
<?xml version="1.0"?>
<button backcol="none" display="label" hotkey_label="yes" label_pos="right" textcol="none">
<label>52498</label>
<tip>how-to-retrieve-the-modification-date-of-a-selected-file-in-a-command-line</tip>
<icon1>#script</icon1>
<function type="script">
<instruction>@script JScript</instruction>
<instruction>// https://resource.dopus.com/t/how-to-retrieve-the-modification-date-of-a-selected-file-in-a-command-line/52498</instruction>
<instruction />
<instruction>function OnClick(clickData) {</instruction>
<instruction> var cmd = clickData.func.command;</instruction>
<instruction> var tab = clickData.func.sourcetab;</instruction>
<instruction> cmd.deselect = false;</instruction>
<instruction />
<instruction> if (!tab) return;</instruction>
<instruction> if (!tab.path) return;</instruction>
<instruction> if (!tab.selected_files.count) return;</instruction>
<instruction />
<instruction> cmd.SetDest(tab.path);</instruction>
<instruction />
<instruction> var cmdLine = 'Copy' +</instruction>
<instruction> ' MOVE' +</instruction>
<instruction> ' COPYFILETIMES=all' +</instruction>
<instruction> ' CREATEFOLDER="{dlgstring|Enter folder name:|' + tab.selected_files(0).modify.Format('D#yyyyMMdd') + ' }"';</instruction>
<instruction />
<instruction> // DOpus.Output(cmdLine);</instruction>
<instruction> cmd.RunCommand(cmdLine);</instruction>
<instruction>}</instruction>
</function>
</button>