question

@DarrylHoar-5879, Welcome to Microsoft Q&A. you could get the instance name from the registry then you could validate the user;s input.

Here is a code example you could refer to:

  private void button1_Click(object sender, EventArgs e)
         {
             RegistryView registryView = Environment.Is64BitOperatingSystem ? RegistryView.Registry64 : RegistryView.Registry32;
             List<string> list = new List<string>();
             using (RegistryKey hklm = RegistryKey.OpenBaseKey(RegistryHive.LocalMachine, registryView))
             {
                 RegistryKey instanceKey = hklm.OpenSubKey(@"SOFTWARE\Microsoft\Microsoft SQL Server\Instance Names\SQL", false);
                 if (instanceKey != null)
                 {
                     foreach (var instanceName in instanceKey.GetValueNames())
                     {
                         Console.WriteLine(instanceName);
                         list.Add(instanceName);
                     }
                 }
             }
             string instancetext = textBox1.Text;
             if(list.Contains(instancetext))
             {
                 MessageBox.Show("The instance name is correct");
             }
             else
             {
                 MessageBox.Show("The instance name is wrong");
             }
         }

Best Regards,
Jack

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I need to be able to programmatically check it in the Service app to verify if the user entered Instance is valid.

There is no way to validate the connection string without attempting to connect to the server.

You could do a brute force connect with a time-out.

Setup a CancellationTokenSource, here to time-out in two seconds

 private static int _timeOut = 2;
 private CancellationTokenSource _cancellationTokenSource =
     new CancellationTokenSource(TimeSpan.FromSeconds(_timeOut));

Method to test connection

 public class Operations
 {
     public static async Task<(bool success, Exception exception)> Connect(string connectionString, CancellationToken cancellationToken)
     {
    
         try
         {
             await using var cn = new SqlConnection(connectionString);
             await cn.OpenAsync(cancellationToken);
             return (true, null);
         }
         catch (Exception e)
         {
             return (false, e);
         }
    
     }
 }

Call it and deconstruct the results

 var (success, exception) = await Operations.Connect("user connection string goes here",_cancellationTokenSource.Token);

Side note, there is always a permission issue, connection string may be good but not assessible to the user.