Effects of nanoparticle size (2.0-6.0 rim) and shape (spherical and cubic) on structural characteristic of atomic ordering processes and order-disorder transformation in B2-type ordered equiatomic-FeCo nanoalloys have been studied by combining electronic theory of alloys in the pseudopotential approximation with Ising-type Hamiltonian site exchange Monte Carlo simulation method. Structural evolutions in amorphous nanopaxticles (2-6 nm) of Fe50Co50 alloy have been utilized via molecular dynamic simulations from room temperatures to 1700 K temperatures. It has been shown that disordering starts at surface and propagates into volume of nanoparticles with increasing temperature. FeCo nanoparticles with critical dimensions more than 5 nm have order-disorder transformation behavior almost similar with bulk B2-FeCo alloys irrespective of their shape. Molecular dynamic analyses indicate that short- and medium-range ordered atomic structures exist in quenched Fe50Co50 nanoparticles at room temperature. Deformed bcc structures and deformed icosahedron structures are most probable atomic configurations for 2, 4, 6 nm particles of Fe50Co50 nanoalloy.