I love Aldi stuff. I don't get the opportunity to shop there very often because we don't yet have a convenient local one and they don't do home delivery. One is being built nearby, to open in the next couple of years. I can't wait, and will almost certainly then largely desert Tesco (which has a near monopoly around here).
I would not change the way I shopped just to pander to these halfwit bullies. As others have said, they only recognise the Aldi goods because they have them at home, and it may help your son to be told this.
Currently, I nearly always buy Tesco home brands, value brands or some of their other recently added discount brands for packet lunches, though I do check out what deals and promotions are going on at the time, in case they are beneficial. I totally refuse to pay several times more for different coloured packaging.
The only one of my three daughters (who all went to state schools) who ever got this mentioned in school was the middle one. She is the least confident of the three and always the one who gets into situations because of that. The other two have just always seemed better equipped to shrug things off and bat away trouble, not outwardly appearing to care quite so much.
Does your son lack a bit of confidence when out of the house? That gives off an air of vulnerability, which bullies such as these soon latch onto. So, maybe they are just looking for a target, and the fact that it is a lunchbox is incidental.
Report them. It is not acceptable behaviour, and as you are presumably paying a substantial sum for your son's education you have a right to expect the school to help out here, and provide an environment where he can feel safe and secure.
I do hope you find a solution which makes him feel better. Whatever it is though, do not give in to them. You are right, and the bullies are wrong.