Eagle software: Different grounds in the same circuit
Your assumption in the second bullet point is correct: that answer does not apply to your situation. The linked question is discussing separate but electrically equal analog and digital ground planes, which is a technique used to reduce electrical noise, not to provide galvanic isolation.

To answer your more general question, you should either use multiple different symbols (you may be able to rename the net for the 'gnd' symbol in Eagle to create different nets; it's a while since I used Eagle), or use named nets for your separate grounds.

Your schematic as shown won't work as intended, however. The isolated side of your optoisolators is powered from a power supply that's (presumably) referenced to the ground of the Arduino side of the circuit.

If you want each of the four circuits to be isolated from each other as well as from the Arduino, you will need a separate power supply for each, and four grounds (plus the Arduino's ground). If you only want to have isolation between the CCFL and Arduino sections of the circuit, you will need a single isolated power supply for the CCFL side - and a single ground in addition to the Arduino's ground.

In every case, remember that you can only use power supplies and signals referenced to the same ground as that part of your circuit.