IIRC you can in Venmo say that its private and thus turn off the weird social thing per payment:
You can also change the default, although that seems to be an option I don't remember having when I first started using the app...
That is located in Settings -> Privacy... although you get a popup saying "You know you can change this per payment, you sure you want to do this" which to me feels weird and pushy.
I agree with Square Cash or other services, instead of Venmo since the whole idea of by default sharing my payments feels weird. Apple Pay works really well too if you and the recipient are both Apple users.