Hi,

I want to provide access to my site to new users as soon as i entered his/her name in the sharepoint list.

Access should be specific to that list only.

This can be done in Sharepoint 2013 ?

Hi,

Do you want that the users who you type name in list items have permission to access the list items which you type users names? Which permission do you want to grant to users?

If you want to grant only view permission to users who you type names in the SharePoint list column to access the list items, you can create a workflow using SharePoint 2010 platform in SharePoint  2013 Designer.You can add Replace List Item Permissions action and click these permissions to add permissions. The value steps are shown as figure below:

The workflow is:

Thanks,

Dean Wang