In this article we will be seeing how to get the User Profile Synchronization 
Connection names from SharePoint 2010.
Through UI you can view the Synchronization connections in Central 
Administration => Application Management =>Manage service applications =>User 
Profile Service Application => Configure Synchronization Connections.
![user.gif]()
Using C# code:
using 
System;
using 
System.Collections.Generic;
using 
System.Linq;
using 
System.Text;
using 
Microsoft.SharePoint;
using 
Microsoft.Office.Server;
using 
Microsoft.Office.Server.UserProfiles;
using 
System.Web;
namespace 
UP
{
    class Program
    {
        static void 
Main(string[] args)
        {
            using (SPSite 
site = new SPSite("http://serverName:12345/"))
            {
             //get the server context
                ServerContext context 
= ServerContext.GetContext(site);
                
UserProfileConfigManager 
upcm = new 
UserProfileConfigManager(context);
           ConnectionManager cm = 
upcm.ConnectionManager;
           foreach (Connection 
cn in cm)
                {
                    Console.WriteLine("Connection 
Name:" + cn.DisplayName.ToString());
                }
                Console.ReadLine();   
            }
        }
    }
}