Yes, It’s possible to retrieve the LoginName of a user if you only have the DisplayName ( Last Name + First Name ).

There are a lot of ways to achieve that like :

1. You can directly query the Active Directory.
2. You can use a PeopleEditor control, which will grab the user if you type in the lastname, firstname combination as follows :
   PeopleEditor people = new PeopleEditor(); people.MultiSelect = false;
   this.Controls.Add(people);
   int userID = Int32.Parse((((PickerEntity)people.ResolvedEntities[0]).EntityData[“SPUserID”]).ToString());
   SPUser user = SPContext.Current.Site.RootWeb.SiteUsers.GetByID(userID);
3. You can use SharePoint Search API ( FullTextSqlQuery Class ) :
   SELECT AccountNameFROM portal..scope()WHERE ( (“SCOPE” = ‘People’) ) AND (“Title” = ‘[DISPLAY NAME]’)

I prefer the third way, much easier.