How can I prove my publication list is mine? In some of the questions regarding author name, it is mentioned that people can use whatever they like, however, they must be consistent across their publications.

When it comes to being hired by a university for a tenure track position or by another principal investigator as a researcher, how can someone prove that they are the author of papers when their author name does not exactly match the one on their ID card? How can a principal investigator be sure that the publication list does actually belong to the person claiming them?
When it comes to hiring a faculty member, you can expect that members of the search committee will look at a candidate's papers.  Since the published paper typically shows the affiliation of the author and the past affiliations of a candidate will appear on the CV, it would generally be obvious if a paper was authored by someone other than the candidate with the same or similar name.  

Of course, a candidate could lie about his/her past affiliations, but we have letters of recommendation and reference phone calls to ensure that doesn't happen.