Assume that I publish many papers in many journals and someday I changed the family name (my last name). How can I edit that where my papers have been published? and is it easy process?
I am afraid that you can't easily change the name on a published article. Publishing is (at least theoretically) still done on print, so there is simply no way to change the physical journal once it has been sent to university libraries all over the world. Even for more important issues such as plagiarism or factually incorrect data, only an errata is issued, or the paper is marked as "retracted".
What you can do instead is advertising the double name on your webpage and CV, and ensuring that the academic databases (such as Web of Science and Scopus) correctly recognize and handle your name change, marking all of your papers as written by a single author. You will probably need to notify them using the "contact us" functions on their websites.
Several authors in the same situation choose to keep the old name also on new papers; this makes it simpler for other researchers to recognize you, at the price of using a name that you might have disowned and now consider a relic from the past. In practice, there is no requirement that your academical nom de plume coincides with the one that is written on your ID and that you use on legal papers, so you are free to sign your papers using a different version of it. Once you choose this route, however, it will be more practical if you consistently use the old name also when attending conferences.
If you are simply getting married, then signing your papers with both surnames is probably the easiest option. (I realize that probably you have already considered and discarded this option, but I thought it more appropriate to include it in my answer anyway.)
As others have pointed out, there is almost certainly no way to change your name in already published papers. In line with the previous answer, I would like to call your attention to initiatives like ORCID and ResearcherID that aim at creating unique identifications for each researcher, so you can collect all your scientific output under a single ID, more or less independently of a particular name or spelling.
There are two strategies that I have heard of that people with renowned accomplishments tend to employ when they get married (what is, I think, the most common situation when a person changes last name). It certainly depends on your legal system, but in my country they either: stay by the old name or use composite last name. The latter meaning that if a person's name was Smith and nupturient's name is Brown, then they change the name to Smith-Brown.