Can I use different brands of Polyurethane on a single project?
I would keep them the same if it's not too inconvenient.

Different manufacturers (and even different batches from the same manufacturer) may have different drying properties (the Satin may come out differently).  They may also have trouble adhering to one another which would lead to cracking between layers and may also yellow differently, producing a blotchy effect later on especially in areas that didn't cover well. 

Your safest bet would have been to buy as much poly as you needed and mix them all together before you started in a seperate container. If you expect the bookshelf to last more than five years then go get the same stuff. Otherwise, it probably doesn't matter.