Nanoplasmonic systems combined with optically active two-dimensional materials provide intriguing opportunities to explore and control light-matter interactions at extreme subwavelength length scales approaching the exciton Bohr radius. Here, we present room- and cryogenic-temperature investigations of a MoSe2 monolayer on individual gold dipole nanoantennas. By controlling nanoantenna size, the dipolar resonance is tuned relative to the exciton achieving a total tuning of similar to 130 meV. Differential reflectance measurements performed on >100 structures reveal an apparent avoided crossing between exciton and dipolar mode and an exciton-plasmon coupling constant of g = 55 meV, representing g/(h omega(X)) >= 3% of the transition energy. This places our hybrid system in the intermediate-coupling regime where spectra exhibit a characteristic Fano-like shape. We demonstrate active control by varying the polarization of the excitation light to programmably suppress coupling to the dipole mode. We further study the emerging optical signatures of the monolayer localized at dipole nanoantennas at 10 K.