there is no OOTB feature in SharePoint 2010 but you can achieve it using Jquery.
Please refer the below links it would help you.
https://www.nothingbutsharepoint.com/sites/eusp/pages/autocomplete-for-sharepoint-people-picker.aspx
Autocomplete people picker in sharepoint2010
http://spjsblog.com/2010/03/25/autocomplete-for-sharepoint-people-picker/
For SharePoint 2013 it works, just wait after typing the name for some seconds. Sometimes it takes time to load the username.
According to your post, my understanding is that autocomplete for people picker field is not working in custom layout form.
People picker loses its autocomplete functionality and defaults to the old style on a form page other than the default form.
As a workflow around, you can add the JavaScript Code to the form page in the SharePoint Designer to add autocomplete functionality.
For more information, you can refer to: Javascript Reference Link
There is a new control called ClientPeoplePicker.
You can change the "<SharePoint:FormField" to "<SharePoint:ClientPeoplePicker
" to display as the new control.
However, you need to add function to get and set the value to the control.
More information:ClientPeoplePicker in SharePoint 2013
Thanks!