It was found that dark matter (DM) in an intermediate-mass-ratio-inspiral (IMRI) system has a significant enhancement effect on the orbital eccentricity of a stellar massive compact object, such as a black hole (BH), which may be tested by space-based gravitational wave (GW) detectors, including LISA, Taiji, and Tianqin in future observations. In this paper, we study the enhancement effect of the eccentricity for an IMRI under different DM density profiles and center BH masses. Our results are as follows: (1) in terms of the general DM spike distribution, the enhancement of the eccentricity is basically consistent with the power-law profile, which indicates that it is reasonable to adopt the power-law profile; (2) in the presence of a DM spike, the different masses of the center BH will affect the eccentricity, which provides a new way for us to detect the BH's mass; and (3) considering the change in the eccentricity in the presence and absence of a DM spike, we find that it is possible to distinguish DM models by measuring the eccentricity at a scale of approximately 10(5)GM/c(2).