In your login page, after user login success select user first name and last name from database using user identity/username. Then create a new session variable named "FullName" and put your first name and last name. see code below maybe code like that.
Code:
string SQLSelect="Select FIRSTNAME,LASTNAME From TABLENAME Where USERNAME="+TxtUserName.Text;
string FullName="Welcome "+NameData.Rows[0]["FIRSTNAME"].ToString()+" "+NameData.Rows[0]["LASTNAME"].ToString();
Session["FullName"] = FullName;
lbldisplay.text = session["FullName"].ToString();
Maybe it's help you.