Spin-split Rashba bands have been exploited to efficiently control the spin degree of freedom of moving electrons, which possesses a great potential in frontier applications of designing spintronic devices and processing spin-based information. Given that intrinsic breaking of inversion symmetry and sizeable spin-orbit interaction, two-dimensional (2D) surface alloys formed by heavy metal elements exhibit a pronounced Rashba-type spin splitting of the surface states. Here, we have revealed the essential role of atomic orbital symmetry in the hexagonally warped Rashba spin-split surface state of $sqrt{3}timessqrt{3} R30^{circ}$ BiCu$_{2}$ monatomic alloy by scanning tunneling spectroscopy (STS) and density functional theory (DFT). From $mathrm{d}I/mathrm{d}U$ spectra and calculated band structures, three hole-like Rashba-split bands hybridized from distinct orbital symmetries have been identified in the unoccupied energy region. Because of the hexagonally deformed Fermi surface, quasi-particle interference (QPI) mappings have resolved scattering channels opened from interband transitions of textit{p$_{x},$p$_{y}$}($m_{j}=1/2$) band. In contrast to the textit{s,p$_{z}$}-derived band, the hexagonal warping predominately is accompanied by substantial out-of-plane spin polarization $S_{z}$ up to 24% in the dispersion of textit{p$_{x}$,p$_{y}$}($m_{j}=1/2$) band with an in-plane orbital symmetry.
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