You can enumerate all servers to find the instance name. Here is an example function to find out the local instance on your machine
Code:
Private Sub Form1_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load
Dim Instance As String = GetLocalSQLService()
End Sub
Private Function GetLocalSQLService() As String
Dim dt As DataTable = Sql.SqlDataSourceEnumerator.Instance.GetDataSources()
For Each dr As DataRow In dt.Rows
If dr.Item("ServerName") = My.Computer.Name Then
Return "MSSQL$" & dr.Item("InstanceName")
End If
Next
Return String.Empty
End Function