Sorry by engraving, do you mean a hot-stamp like at LV? Or do you mean embroidery?
I know some boutiques have foil-stamped Lady Dior bags before (the leather circle behind the DIOR charms) and it is complimentary, although I don't think that all boutiques do it.
Dior has an even better personalization service called ABCDior which includes embroidering your name on the Book Tote and woven Lady Dior bags. This service extends even to their WalkN'Dior shoes (the customization will go on a woven fabric strip which will then be attached to the back of the shoe). This service is not free, though, although it is one the best name customizations I have seen from any designer brand. For the Book Tote in Canada, the personalization adds another $300 to the Book Tote.