I’ve never heard of wrapping a CD or tape before discarding it. I suppose a memory card would be the same, but since none contain actual letters and words, I’ve never heard that they can’t be disposed of normally. They’re not shaimos. Are they being considered as tashmishei mitzvah, such as wood from a sukkah or worn out tzitzis? Interesting.
As far as erasing Hashem’s name from a typical screen, most poskim have said it’s not a problem, and I understand that the reason is because the screen is constantly refreshing. In other words, it flashing on and off very quickly (too fast for our eyes to perceive) so when you turn it off, you’re not actually erasing it, you’re causing it to not flash back on.
Some screens (such as Kindle Paperwhite I believe) use what’s called e-ink, and turning a page or turning it off does actually erase.
I believe R’ Dovid Feinstein said these would be a problem if there’s Hashem’s name on it.
There was a problematic electronic “seforim library” device made with this technology. I don’t know if it’s still made.