I think this is the fastest and easiest way. Use the Bezier Tool and create the shape of your logo. Add a Particle such as “Basic Smoke”. F4 for the Emitter tab. Shape = Geometry. Drag the shape you created into the Shape source well. Disable the shape so you no longer see it. The particle will conform to the shape you created.

PS. You can do Image instead of Geometry but…”Particles emerge from within an area defined by an image or from only the edges of the image. The image may or may not have an alpha channel. If it does, the shape of the alpha channel can also be used to define the emitter shape. The Image shape displays additional parameters.”
Hope this helps.
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