After the detection of GRB 170817A, the first unambiguous off-axis gamma-ray burst (GRB), several studies tried to understand the structure of GRB jets. The initial jet structure (directly produced by the central engine) can be partially preserved, or can be completely modified by the interaction with the environment. In this study, we perform three-dimensional, special relativistic hydrodynamics simulations of long GRB jets evolving through a massive progenitor star. Different jet scenarios were considered: Top-hat, Gaussian jets dominated by pressure or by kinetic energy, as well as a model of a supernova (SN) plus a jet both propagating through the progenitor. We found that, while propagating inside the progenitor star, jets with different initial structures are nearly indistinguishable. Kinetic dominated jets are faster and more collimated than pressure dominated jets. The dynamics of jets inside the progenitor star strongly depends on the presence of an associated SN, which can substantially decelerate the jet propagation. We show that the initial structure of GRB jets is preserved, or not, mainly depending on the jet collimation. The initial structure is preserved in uncollimated jets, i.e. jets which move through low density environments. Meanwhile, jets which move through dense environments are shaped by the interaction with the medium and remain collimated.