string path = AppDomain.CurrentDomain.BaseDirectory;
string[] filePaths = Directory.GetFiles(path, "*.txt");
foreach (string file in filePaths)
{
    cboLanden.Items.Add(file);
}
This is my code and it returns the full path, I would like to have only the name, without the path in my combobox.
Use Path.GetFileName() to get file name without path:
string path = AppDomain.CurrentDomain.BaseDirectory; 
string[] filePaths = Directory.GetFiles(path, "*.txt"); 
foreach (string file in filePaths) 
{ 
   cboLanden.Items.Add(Path.GetFileName(file)); 
}
Also consider to use files as data source of your comboBox:
 cboLanden.DataSource = Directory.EnumerateFiles(path, "*.txt")
                                 .Select(Path.GetFileName)
                                 .ToList();
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