Like another poster said, if you're worried about privacy/data collection/spam, just sign up with false details. Now days, everything is done through the app so you can get all the benefits without using a real identity.
Also, if you use Apple Pay / Android Pay, a device account number (DAN) is generated that is different from your physical card number. I'm not sure whether retailers get a name from such a transaction, but I suspect they just get the card number?
As for the app, I don't want my phone polluted with even more crap. If I had a corporate loyalty app for every shop I wanted to go in, I'd have a hundred apps, a hundred data collection problems and a flat battery. Instead I have one called Apple Pay which works everywhere..
Personally I find the Sainsbury's scheme (Nectar) better overall, however. All the "vouchers" that multiply your points are applied automatically through the app, rather than having to goof around with scanning barcodes as in the Tesco app.
I haven't worked out my exact spend at Sainsbury's this year, but it was probably less than £1000. From that I had enough nectar points to buy £100 worth of wines in a recent promotion, and I still have plenty left over... (points, that is. Most of the wine is gone, haha)