Unraveling competing charge orders in monolayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>VTe</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math>

Multiple charge density waves (CDWs) are observed in monolayer ${\mathrm{VTe}}_{2}$, but its modulated lattice and electronic structures remain less explored. Here, we identify $4\ifmmode\times\else\texttimes\fi{}4$, $2\sqrt{3}$ $\ifmmode\times\else\texttimes\fi{}$ $2\sqrt{3}$, and related stripe CDW phases of monolayer ${\mathrm{VTe}}_{2}$ and clarify their relative stability using first-principles calculations. On top of a $4\ifmmode\times\else\texttimes\fi{}4$ star-of-David (soD) phase showing unstable zone-center optical phonon modes, we find two lower-energy $4\ifmmode\times\else\texttimes\fi{}4$ distorted soD phases, preserving (or breaking) threefold rotational symmetry and having nontrivial ${Z}_{2}$ = 1 (or trivial) band topology, with simulated scanning tunneling microscopy patterns agreeing with experiments on samples with corresponding symmetry. We confirm their metallic CDW behaviors with distinct $k$-resolved gapping characters, and reveal the possible superimposition of a $4\ifmmode\times\else\texttimes\fi{}1$ stripe phase on the $4\ifmmode\times\else\texttimes\fi{}4$ order. The $2\sqrt{3}$ $\ifmmode\times\else\texttimes\fi{}$ $2\sqrt{3}$ phase featuring a continuous pattern of truncated triangle-shaped V clusters is less stable in energy than $4\ifmmode\times\else\texttimes\fi{}4$ phases, and behaves as a semimetal within semilocal functional, but as a small-gap semiconductor when including the nonlocal exchange interaction, in line with experiments. We further unravel the effects of charge doping and potential magnetic interactions on the energy sequence and precedence of different CDW phases. Our work provides important insights into the competing charge orders in monolayer ${\mathrm{VTe}}_{2}$, paving the way for future experiments and device designs.