As per your requirment, you need show list of existing group names as suggestion in the NewItemForm page of that list.
To achieve this you can use jQuery UI AutoComplete feature.
It will show list of unique groups in a dropdown list which user can either select a value from the list OR they can enter their own value in the textbox.
Hope this is what you want to acheive.
Following is code snippet which you have to include inside a content editor web part on that page.
<link rel="stylesheet" href="http://code.jquery.com/ui/1.10.3/themes/smoothness/jquery-ui.css" />
<script type="text/javascript" src="https://code.jquery.com/jquery-1.11.0.min.js "></script>
<script type="text/javascript" src="http://code.jquery.com/ui/1.11.2/jquery-ui.js"></script>
<script type="text/javascript">
$(document).ready(function () {
SP.SOD.executeOrDelayUntilScriptLoaded(init, "sp.js");
});
function init(){
$.ajax( {
method: 'GET',
url: _spPageContextInfo.webAbsoluteUrl + "/_api/web/lists/getByTitle('myListName')/items?$select=Title",
contentType: "application/json; odata=verbose",
headers: {
"Accept": "application/json; odata=verbose"
},
success: function( data ) {
var arr = [];
for(var i = 0; i < data.d.results.length; i++){
arr.push(data.d.results[i].Title);
}
arr = $.unique(arr); // returns array with unique values
$("input[type=text][title='Title']").autocomplete({
source: arr,
minLength:0
}).focus(function(){
$(this).data("uiAutocomplete").search($(this).val());
});
},
error: function(e){
console.log("Error");
console.log(e);
},
});
}
</script>
Single Line of Text
ORChoice
where users allowed to add their own entry in dropdown? Also are you showing the existing values in DropDown in a custom New Item Form?