In this outdated but seemingly comprehensive guide to creating an altcoin fork of bitcoin they make special mention of the need to change the rpc port.

Although in the intervening time the file names have changed the variables remain so I think this advice is still valid.

What is the purpose of these ports? What information do they transmit? Why are they there and why must we change them when creating a new network?

Step 4- Ports(required)

a) bitcoinrpc.cpp 
    -change RPC port.

    Code:
    ip::tcp::endpoint endpoint(bindAddress, GetArg("-rpcport", 55883));

    Code:
    if (!d.connect(GetArg("-rpcconnect", "127.0.0.1"), GetArg("-rpcport", "55883")))

b) init.cpp
   -change RPC port

    Code:
    -rpcport= " + _("Listen for JSON-RPC connections on  (default: 55883)") + "\n" +

    -change Testnet and Common port(P2P).

    Code:
    -port= " + _("Listen for connections on  (default: 55884 or testnet: 45884)") + "\n" +

c) protocol.h

  -Testnet and P2P port again.

    Code:
    return testnet ? 45883 : 55884;