The ultrafast concentration of electromagnetic energy in nanoscale volumes is one of the key features of optical nanoantennas illuminated at their surface plasmon resonances. Here, we drive the insulator to metal phase transition in vanadium dioxide (VO2) using a laser-induced pumping effect obtained by positioning a single gold nanoantenna in proximity to a VO2 thermochromic material. We explore how the geometry of the single nanoantenna affects the size and permittivity of the nanometer-scale VO2 regions featuring phase transition under different pumping conditions. The results reveal that a higher VO2 phase transition effect is obtained for pumping of the longitudinal or transversal localized surface plasmon depending on the antenna length. This characterization is of paramount importance since the single nanoantennas are the building blocks of many plasmonic nanosystems. Finally, we demonstrate the picosecond dynamics of the VO2 phase transition characterizing this system, useful for the realization of fast nano-switches. Our work shows that it is possible to miniaturize the hybrid plasmonic-VO2 system down to the single-antenna level, still maintaining a controllable behavior, fast picosecond dynamics, and the features characterizing its optical and thermal response.