Metal nanorods show excellent optical properties, since the plasmonic resonance frequency can be tuned by its aspect ratio and the optical field can be confined within a region of subwavelength, even within a nanometer region. It has the ability to flexibly modify the spontaneous emission properties of a nearby quantum emitter. However, it is unclear how the emission property changes when the metal nanorod has been deposited at the tips or coated on all sides with metal. In this work, the spontaneous emission enhancements of a two-level atom around a tailored nanorod with a wide variety of shapes, dimensions or materials are systematically investigated by the finite element method. Three different optical response models are adopted, including the classical local response approximation (LRA), the nonlocal hydrodynamic model (HDM), and the generalized nonlocal optical response model (GNOR). For a cylindrical nanorod with two endcaps, it is found that the resonance frequency shows large redshift and the emission enhancement peak increases as the endcap gradually changes from cone to cylinder of the same height. The resonance frequency shows small blueshift and the emission enhancement peak decreases slightly as the deposited metal of the conical endcaps changes from gold to silver. However, as the material of the cylinder also changes from gold to silver, becoming an all-silver nanostructure, an obvious blueshift can be detected at the resonance frequency and the emission enhancement peak rises sharply. For bimetal core-shell nanostructure, the shell can screen the surface plasmon of the core from being excited, and the plasmonic resonance associated with shell increases in proportion to the thickness of the shell. The emission enhancement peak for gold nanostructure appears to be blue-shifted when coated with silver. In contrast, it is red-shifted for silver nanostructure coated with gold.