I'm trying to find out the correct name for the brake levers that are on a bike so that you can ride in a nearly upright position? I had an old Schwinn 10 speed that not only had the regular brake levers on the drop down handlebars, but it also had a set so you use them when you're riding in an upright position? I'm hoping someone can tell me what they're called from my vague description? Thanks
There are two sorts of brake lever that would suit this description - given mention an older ten speed you're probably remembering these:
Not recommended unless you're going for original-look. I have one on my 80s bike and its just for show - I never use it.
These brake levers work fine, and function either in concert with dropbar brake/shifters as pictured, or can be used as brake levers by themselves if you're on a flatbar bike.
Again, these are mostly cable-brake based, but there are also hydraulic versions of the interruptor brake. Shimano's GRX groupset has them as an option.
Given you're looking for a new bike, this doesn't fit your need, but...
The third option is to either learn to brake with existing drop bar brakes, or look at upgrading to more modern brifters. The difference there is that the whole hand position has improved over time, and now braking from the hoods position works much better than older dropbar brakes.
See also Braking on a vintage road bike