SSMS connection string
Connection to named instances is handled by SQL Browser Service:


  When an instance of SQL Server starts, if the TCP/IP or VIA protocols
  are enabled for SQL Server, the server is assigned a TCP/IP port. If
  the named pipes protocol is enabled, SQL Server listens on a specific
  named pipe. This port, or "pipe," is used by that specific instance to
  exchange data with client applications. During installation, TCP port
  1433 and pipe \sql\query are assigned to the default instance, but
  those can be changed later by the server administrator using SQL
  Server Configuration Manager. Because only one instance of SQL Server
  can use a port or pipe, different port numbers and pipe names are
  assigned for named instances, including SQL Server Express. By
  default, when enabled, both named instances and SQL Server Express are
  configured to use dynamic ports, that is, an available port is
  assigned when SQL Server starts. If you want, a specific port can be
  assigned to an instance of SQL Server. When connecting, clients can
  specify a specific port; but if the port is dynamically assigned, the
  port number can change anytime SQL Server is restarted, so the correct
  port number is unknown to the client.
  
  Upon startup, SQL Server Browser starts and claims UDP port 1434. SQL
  Server Browser reads the registry, identifies all instances of SQL
  Server on the computer, and notes the ports and named pipes that they
  use. When a server has two or more network cards, SQL Server Browser
  returns the first enabled port it encounters for SQL Server. SQL
  Server Browser support ipv6 and ipv4.
  
  When SQL Server clients request SQL Server resources, the client
  network library sends a UDP message to the server using port 1434. SQL
  Server Browser responds with the TCP/IP port or named pipe of the
  requested instance. The network library on the client application then
  completes the connection by sending a request to the server using the
  port or named pipe of the desired instance.