Recently I got a cite in a research paper where the author cited my work as [first name] et al, where it should have been [last name] et al. Is there any problem for indexing purpose? should I contact the journal editor about this incident and ask for correction?
Yes, that's a problem, and you will absolutely want to fix it. The problem is that it's actually a two-stage problem to correct:
- First, you will need to contact the journal to fix the citation.
- Then, after the citation has been corrected in the article, you'll need to submit a correction request to the various citation trackers (such as ISI and Scopus). They will need to fix your citation in their database, if the article has already been entered.
Note: It may or may not be possible to correct the journal—the editors may or may not be willing to issue a correction to fix a reference. However, it may be possible to correct the reference with the citation indices, even if it's not correct in the journal. However, the road will be tougher; you'll need to show that the paper that should be cited is indisputably yours.
In addition to the earlier answer, you may also want to email the authors of the paper and inform them of their error, providing the correct bibliographic information, to prevent the problem in the future.