Hi condurat.catalir, welcome to the Sony Forums
LIke many modern digital cameras, the W510 does not have a date-stamp function. What you see on the built-in screen is only for review and display purposes.
However, assuming you're using Sony PMB to download your photos, you should be able to add a date stamp once the image is on your PC. See the following tutorial for details:
http://support.d-imaging.sony.co.jp/www/disoft/int/pmb/feature/edit/attach_date.html
PMB for the W510 can be downloaded here: http://www.sony.co.uk/support/en/product/DSC-W510/downloads/PMB
Hope that helps 
Mick