We measure the luminosity functions (LFs) and stellar mass functions (SMFs) of photometric satellite galaxies around spectroscopically identified isolated central galaxies (ICGs). The photometric satellites are from the DESI Legacy Imaging Surveys (DR9), while the spectroscopic ICGs are selected from the DESI Year-1 BGS sample. We can measure satellite LFs down to r-band absolute magnitudes of Mr,sat ∼ ‑7, around ICGs as small as 7.1<log10M∗,ICG/M⊙<7.8 , with the stellar mass of ICGs measured by the DESI FASTSPECFIT pipeline. The satellite SMF can be measured down to log10M∗,sat/M⊙∼5.5 . Interestingly, we discover that the faint/low-mass end slopes of satellite LFs/SMFs become steeper with the decrease in the stellar masses of host ICGs, with smaller and nearby host ICGs capable of being used to probe their fainter satellites. The steepest slopes can be ‑2.298 ± 0.656 and ‑2.888 ± 0.916 for satellite LF and SMF, respectively. Detailed comparisons are performed between the satellite LFs around ICGs selected from DESI BGS or from the SDSS NYU-VAGC spectroscopic Main galaxies over 7.1<log10M∗,ICG/M⊙<11.7 , showing reasonable agreement, but we show that differences between DESI and SDSS stellar masses for ICGs play a role to affect the results. We also compare measurements based on DESI FASTSPECFIT and CIGALE stellar masses used to bin ICGs, with the latter including the modeling of active galactic nuclei based on Wide-field Infrared Survey Explorer photometry, and we find good agreements in the measured satellite LFs by using either of the DESI stellar mass catalogs.