Put picture from imported pic as vertex paint and engrave / extrude the shape from other object What we have:
We imported image as a plane from PNG. Originally white presented on this import supposed to be transparent but after import it appears white.



What we need:


How to embed the image from this texture onto the cube as vertex paint and remove white background which on original png is transparent?
How to extrude in the shape of this logo into the cube (with/without color - so it appears like this "itoma" logo is written couple of millimeters inside the face of the cube)?
How to extrude out the shape of this logo outside of the cube with or without color - so it appears like this "itoma" logo is written couple of millimeters outside one face of the cube - sticking out?
Usually this is how I do it....

Convert the Jpg or Png into SVG format. You can find a
free online converter on google search. Keyword to search
is "Converter Jpeg to SVG" or "Converter Png to SVG".

You can then import the SVG format as a spline. With the
spline, you could then convert it to mesh. Fill those faces
and extrude those faces.

To cut the words into a cube, you would use the boolean or
booltool ( An easier and a better way to work) in Blender
to accomplish the task.

NOTE:

You may have to watch a few topics on youtube on the subject
I have pointed you to. Else there will be too much instruction
to write up.