We present the results of our identification of eight objects from a preliminary catalogue of X-ray sources detected in the 4-12 keV energy band by the Mikhail Pavlinsky ART-XC telescope aboard the SRG observatory during its first all-sky survey. Three of them (SRGAJ005751.0+210846,SRGAJ014157.0-032915, SRGAJ232446.8+440756) have been discovered by ART-XC, while five were already known previously as X-ray sources, but their nature remained unknown. The last five sources have also been detected in soft X-rays by the eROSITA telescope of the SRG observatory. Our optical observations were carried out at the 1.6-m AZT-33IK telescope of the Sayan Observatory and the 1.5-m Russian-Turkish telescope (RTT-150). All of the investigated objects have turned out to be active galactic nuclei (AGNs) at redshifts from 0.019 to 0.283. Six of them are Seyfert 2 galaxies(including one Seyfert 1.9 galaxy), one (SRGAJ005751.0+210846) is a hidden AGN (in an edge-on galaxy), and one (SRGAJ224125.9+760343) is a narrow-line Seyfert 1 galaxy. The latter object is characterized by a high X-ray luminosity (~(2-13)*10^44 erg/s in the 4-12 keV band) and,according to our black hole mass estimate (~2*10^7 M_sun), an accretion rate close to the Eddington limit. All three AGNs discovered by the ART-XC telescope (which are not detected by the eROSITA telescope) are characterized by a high absorption column density (N_H > 3*10^23 cm^-2). The results obtained confirm the expectations that the ART-XC telescope is an efficient instrument for searches of heavily obscured and other interesting AGNs in the nearby (z<0.3) Universe. The SRG all-sky survey will last for more than 3 years more, which will allow many such objects to be discovered.