I have a text in yellow background but the eraser tool erases with white colour.
How can I set it to erase with the yellow background?
The Eraser Tool doesn't erase with any colour in Inkscape. If you switch on the Chequered Background option in the Document Properties, you will see what is really going on.
The Eraser Tool in Inkscape basically cuts through vector objects. It doesn't use pixels, and doesn't create any colours, unlike how it can be used in raster image editors such as GIMP or Photoshop in some circumstances.
Example
If you want to Erase through the text only, leaving the yellow background object intact, you can lock the rectangle in the Objects panel before using the Eraser Tool. Locking an object prevents it from being selected or edited.
Example
