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Plasmonics in two-dimensional materials, an emerging direction of nano-optics, has attracted great attention recently, which exhibits unique properties than that in noble metals. Extending its advanced features by different manipulations is very beneficial for its promotion. In this paper, we study plasmonic excitations in graphene and black phosphorus (BP) nanostructures, where the effects of structural symmetry and material anisotropy are discussed. We show that the two factors are crucial to mode excitations, e.g. the extinction can be dominated by higher order modes rather than dipole resonance. The behavior occurs only in the direction hosting larger resonance frequencies, e.g. armchair (AC) direction of BP and shorter side of graphene rectangles. In BP rectangles along AC direction, the two factors are competing, and thus can be applied cooperatively to tune plasmonic resonance, from dipole to higher order excitations. Besides, the manipulation can also be achieved by designing BP square rings, in which the interaction between outer and inner edges show great impact on mode excitations. Our studies further promote the understanding of plasmonics in two-dimensional materials, and will pave the way for particular plasmonic applications.