Recently I have purchase a cotton bed sheet but I was not able to sleep on it for the color is not fast and it has already destroy my night suit and my skin color also becomes the color of my bed sheet.
Please let me know how can I treat to make it color fast. I shall be grateful if you also give me the name of dye/color/chemical name.

There is no possible way I could even begin to guess what kind of the thousands of different dyestuff was used to dye your sheet. However, it was not applied properly, or it would not be rubbing off. Crocking of dye, as this is called, is a sign of incompetent dyeing; the sheet should be returned to the manufacturer and replaced with one that is properly dyed.

You might be able to salvage the sheet by washing it many times in hot water, and then treating it with a cationic fixative such as Retayne, which, at least in the US, is generally available from quilting supply stores, and may also be purchased by mail-order from many of the companies listed on my Sources for Dyeing Supplies page. Also see "Is there anything I can do to "set" the dye on purchased fabric?".

The one dye that is most likely to be misapplied so that it rubs off is indigo, whether natural or synthetic. It is essential, when dyeing with indigo, to subject the fabric to multiple dyeings with small amounts of dye, rather than one dyeing with a great deal of dye. However, any dye will do this if it is not applied correctly and excess unattached dye is not washed out before use. It is the reponsibility of the dyer to make sure that this is done, or else give instructions for fabric care that will prevent problems.