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labels = Table[i -> Style[Subscript[v, i], 20], {i, 3}]
names = Table[i -> "longname_" <> "v_" <> ToString@i, {i, 3}];
colors = {1 -> Blue, 2 -> Red, 3 -> Green}; 

legend = SwatchLegend[Last /@ colors, 
      Row[{#[[1]], ": ", #[[2]]}] & /@ Transpose[{labels, names}][[All, All, -1]],
      LegendMarkers -> "Bubble"];

You can use Legended, Epilog or Row to add legends to a Graph:

Legended[Graph[{1 <-> 2, 2 <-> 3,  3 <-> 1},  VertexSize -> 0.1,
                VertexStyle -> colors, VertexLabels -> labels, ImagePadding -> 20], 
         legend]

Graph[{1 <-> 2, 2 <-> 3, 3 <-> 1},
    VertexStyle -> colors, VertexSize -> 0.1, VertexLabels -> labels, 
    ImagePadding -> 20, 
 Epilog -> Inset[legend, {.75, .75}]]

Row[{Graph[{1 <-> 2, 2 <-> 3, 3 <-> 1}, VertexStyle -> colors, VertexSize -> 0.1, 
            VertexLabels -> labels, ImagePadding -> 20, ImageSize -> 300], 
    legend}]