When a paper appears in a science journal, why do not mention the names of the reviewers so that we, as readers can get an idea about the seriousness of the paper?
There are at least two reasons that reviewing is anonymous.
The first, probably less important, reason is that we want reviews to be honest and immune from any pressure. Some junior academics in fact wind up reviewing papers by senior members of the profession. We don't want pressure applied before the review is complete, nor retaliation afterwards.
But, in my view, the more important reason is that a paper should speak for itself. It either says something significant or it does not. The opinions of others should weigh less than the statements in the paper itself in the final analysis. If a well respected academic wrongly promotes a paper, harm can be done. Mistakes can be made. Let the paper itself stand or fall on its own.
Some journals do, such as the Frontiers journals; here's an article I wrote that names the reviewers at the bottom. But the reason most journals don't is that this compromises the anonymity of reviewers, which is widely considered necessary to protect reviewers from reprisal from bad reviews. Personally, I think the benefits of transparency outweigh these dangers and hence reviews should be non-anonymous (I sign all my reviews, so long as journal policy permits me to), but I'm in the minority here.
The general idea behind anonymity of a review is that the reviewer can write his/her opinion without being concerned that that the author is offended (and will potentially revenge in some way).
Having said that there are some journals that do publish reviewers names, for example Frontiers: https://www.frontiersin.org/articles/10.3389/fcell.2018.00102/full (see top left corner). There are also journals that publish reviews and the rebuttal of the author, for example eLife: https://elifesciences.org/articles/39865 (see decision letter and author response sections). But this is usually done without reviewers' names.
Given that then, plus the fact that knowing the name of the reviewer can lead to a potential backlash down the road (can you remain impartial if the same reviewer is consistently recommending rejection for your work?), this is not necessarily a good change to make.