Laser irradiation of metals is widely used in research and applications. In this work, we study how the material geometry affects electron-phonon coupling in nano-sized gold samples: an ultrathin layer, nano-rod, and two types of gold nanoparticles: cubic and octahedral. We use the combined tight-binding molecular dynamics Boltzmann collision integral method implemented within XTANT-3 code to evaluate the coupling parameter in irradiation targets at high electronic temperatures (up to Te~20,000 K). Our results show that the electron-phonon coupling in all objects with the same fcc atomic structure (bulk, layer, rod, cubic and octahedral nanoparticles) is nearly identical at electronic temperatures above Te~7000 K, independently of geometry and dimensionality. At low electronic temperatures, reducing dimensionality reduces the coupling parameter. Additionally, nano-objects under ultrafast energy deposition experience nonthermal damage due to expansion caused by electronic pressure, in contrast to bulk metal. Nano-object ultrafast expansion leads to ablation/emission of atoms, and disorder inside of the remaining parts. These nonthermal atomic expansion and melting are significantly faster than electron-phonon coupling, forming a dominant effect in nano-sized gold.