Q: Should I inform the editor about my change of affiliation if my paper has already been published?

Generally speaking, the affiliation should reflect the institution that sponsored your research and where you did the maximum part of your research work.  In that sense, there is actually no need to change your affiliation. However, the affiliation has another purpose: if someone wants to contact you as the author of the paper, they know where to find you.

If your affiliation has changed, your institutional email address would also change and this might make it difficult for readers to reach you if they want. Therefore, I think it might be a good idea to write to the editor of the journal informing him/her about your change of affiliation and providing your new email address.  

Once a paper is published, the affiliation cannot usually be changed. But if the editor is informed about your change of affiliation, he/she can at least direct readers to your new address in case they wish to contact you.

Related reading:

• How should I list multiple affiliations in my paper?
• What should my affiliation be if I changed my workplace during a manuscript submission?