I don't know the answer, however here are a couple of ideas:

Changing SH3D code
The method paintIcon() in PlanComponent.java appears to generate an image which is used as a "proxy" for an item of furniture. Perhaps you could rewrite that method to create a little text label which displays the name of the item

PostProcessing the SVG
I've exported an SVG file and it consists of vector graphics and <image .../> tags which I believe are "proxy" images. I removed the images with this:

$ cat SGx.svg | xmllint --format --recover - | sed 's#<image.*/>##g' > SGy.svg

I suspect the <image ../> tag is identical for every instance of the same item of furniture. A script could be devised to identify every <image ../> and replace it with a graphical/SVG text label unique for that <image ../>