Suppose that pointsthese are lists of coordinates and a labelslist of corresponding labels, for example,
points = Flatten[Table[{i, j, Sin[i j]},
{i, 0, Pi, Pi/20}, {j, 0, Pi, Pi/10}], 1];
labels = RandomChoice[{"label a", "label b", "label c"}, Length[points]];
, , .
rules = {"label a" -> RGBColor[1, 1, 0],
"label b" -> RGBColor[1, 0, 0], "label c" -> RGBColor[1, 0, 1]};
, ,
ListPointPlot3D[Pick[points, labels,
PlotStyle -> Union[labels] /. rules]

Edit
ListPlot3D, VertexColors,
ListPlot3D[points, VertexColors -> labels /. rules, Mesh -> False]
