there is no OOTB feature in SharePoint 2010 but you can achieve it using Jquery.
Please refer the below links it would help you.
Autocomplete people picker in sharepoint2010
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.
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