Pseudo code it out.

User Input
1. Check for null or empty entry
   A. Is valid input?
      a. yes then continue
      b. no
         i. Display error message
         ii. do not continue processing
2. Process Input

Process Input
1. Determine Abbr vs Full Name (Length?)
   A. Abbr = true
      a. Loop through array of countries (For .. Next?)
      b. Does it match?
         i. yes then matchfound = true
         ii. no then continue loop
   B. Full name = true
      a. Loop through array of countries
      b. Does it match?
         i. yes then matchfound = true
         ii. no then continue loop
2. Is matchfound = true?
   A. Yes
      a. Display abbr or fullname or both
   B. No
      a. Display error message

Once you understand the steps (pseudo code) then you can start applying code.
Pseudo code will also help you to identify parts that can be factored out to separate methods or functions.

To split the string

Dim splitString() As String = naam.Split()
'This gives you an array of values
'splitString(0) = "william"
'splitString(1) = "lemeer"

Using the above code to perform the split you then build your SQL statement. (and since you don't include which provider we'll assume SQL)

     Dim splitString() As String = naam.Split()
     'This gives you an array of values
     'splitString(0) = "william"
     'splitString(1) = "lemeer"

     'Make the SQL query string
     Dim queryString = "SELECT personeelnr FROM personeel WHERE personeel.naam =@firstName AND personeel.achternaam = @lastName"

     'create our database connection and the command object that we will use
     Using connection As New SqlConnection(connectionString)
          Using command As New SqlCommand(queryString, connection)

               'check if the connection is open, if not then open it
               If Not connection.State = ConnectionState.Open Then
                    connection.Open()
               End If

               'Add parameters
               command.Parameters.AddWithValue("@firstName", splitString()))
               command.Parameters.AddWithValue("@lastName", splitString(1))

               'Get the reader object
               Dim reader As SqlDataReader = command.ExecuteReader()

               'Fill a table of values
               Dim dtResults As New DataTable("Results")
               dtResults.Load(reader)
          End Using
     End Using

And why would you want to keep the user of the computer from being able to access a legitimate program through the intended use of its systray icon?

Don't turn Option Strict to off, leave it on -- it will save you time in the future.

My list:

Space Above and Beyond - it was great ( I am also a fan of the movie Soldier)
SG-1
SG-Atlantis
Firefly
Flash Forward
Spellbinder