You could insert script editor/content editor webpart to your list form, and init the field value by javascript.
<script src="//ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
<script type="text/javascript">
$(document).ready(function () {
var userid = _spPageContextInfo.userId;
function GetCurrentUser() {
var requestUri = _spPageContextInfo.webAbsoluteUrl + "/_api/web/getuserbyid(" + userid + ")";
var requestHeaders = { "accept": "application/json;odata=verbose" };
$.ajax({
url: requestUri,
contentType: "application/json;odata=verbose",
headers: requestHeaders,
success: onSuccess,
error: onError
});
}
function onSuccess(data, request) {
var loginName = data.d.Title;
SetUserFieldValue("people", loginName);
}
function onError(error) {
//alert(error);
}
function SetUserFieldValue(fieldName, userName) {
var _PeoplePicker = $("div[title='" + fieldName + "']");
var _PeoplePickerTopId = _PeoplePicker.attr('id');
var _PeoplePickerEditor = $("input[title='" + fieldName + "']");
_PeoplePickerEditer.val(userName);
var _PeoplePickerObject = SPClientPeoplePicker.SPClientPeoplePickerDict[_PeoplePickerTopId];
_PeoplePickerObject.AddUnresolvedUserFromEditor(true);
}
GetCurrentUser();
});
</script>