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In RegionPlot you can do

RegionPlot[{x^2 < y^3 + 1, y^2 < x^3 + 1}, {x, -2, 5}, {y, -2, 5}, PlotLegends -> "Expressions"]

enter image description here

But this seem to not work for RegionPlot3D

RegionPlot3D[{x - 0.5*y + z <= 0, x + y + z <= 0}, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, AxesLabel -> {"x", "y", "z"}]

enter image description here

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A general way to do this, that allows you to play with colors and transparencies:

Show[
 RegionPlot3D[x - 0.5*y + z <= 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
  AxesLabel -> {"x", "y", "z"}], 
 RegionPlot3D[x + y + z <= 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
  AxesLabel -> {"x", "y", "z"}]]

Mathematica graphics

For the intersection:

RegionPlot3D[
 x - 0.5*y + z <= 0 && x + y + z <= 0, 
{x, -2, 2}, {y, -2, 2}, {z, -2, 2}, AxesLabel -> {"x", "y", "z"}]

Mathematica graphics

and union :

RegionPlot3D[
 x - 0.5*y + z <= 0 || x + y + z <= 0, 
{x, -2, 2}, {y, -2, 2}, {z, -2, 2}, AxesLabel -> {"x", "y", "z"}]

Mathematica graphics

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