Set User context in Email Template

Question

I would know if it's possible set a "User" for an email template.

In a my email template I use {!User.Name}. I have a class and a trigger on CollaborationGroupMember and I send an email each time that a user is added in a chatter group:

Class

public with sharing class ClassToSendMail {

    public static void sendMail(String emailTemplate, String mailRecipient, Id targetObjectID) {

        Id templateId; 
        templateId = [select id, name from EmailTemplate where developername = : emailTemplate].id;

        OrgWideEmailAddress owa = [select id, Address, DisplayName from OrgWideEmailAddress limit 1];

        Messaging.SingleEmailMessage email = new Messaging.SingleEmailMessage();
        String[] toRecipients = new String[]{'[email protected]'};

        email.setToAddresses(toRecipients);
        email.setOrgWideEmailAddressId(owa.id);
        email.setTargetObjectId(targetObjectID);
        email.setTemplateId(templateId);    
        email.setSaveAsActivity(false);

        try 
        {
            Messaging.sendEmail(new Messaging.SingleEmailMessage[] {email});
        }
        catch (EmailException e) {String errorMsg='Error in : '+e.getMessage();}
    }
}

Trigger

trigger TriggerSendMail on CollaborationGroupMember (after insert) {
    for(CollaborationGroupMember newMember : Trigger.new){
        System.debug('@@@ newMember: ' + newMember);
        User userToSendMail = [SELECT id, Email FROM User WHERE ID=:newMember.MemberID];
        ClassToSendMail.sendMail('UserAddedGroup', userToSendMail.Email , userToSendMail.Id);
    }
}

When I add an user in a chatter group, {!User.Name} is replace with name of the current user logged in org and not the user set as targetObject.