Discussing Related Work: Use of the phrase 'the authors'
It sounds like you have a sensible reason why you shouldn't just replace the phrase "the authors" with the names, without making any other edits.  Introducing the names abruptly would read strangely if it happens several paragraphs into the discussion, since it wouldn't be clear who these people are.

You can solve this problem by introducing the names earlier.  Instead of opening with "In [1] a system is described...", you could use "Jones and Smith [1] developed a system..." or another variant.

There are several advantages to this:


It provides more context for readers.  In particular, it's easier to recognize the names Jones and Smith than a reference like [1], so readers who have heard of this work before can catch on more quickly without having to flip to the references.
It is more generous in offering credit to the authors.  Too much use of the passive voice and phrases like "the authors" could even look like you are going out of your way to avoid naming them.  (I don't think most people would be upset about that, but it could be an issue if the authors are particularly touchy.  I've occasionally known people who were irritated by how they were cited in situations that seemed innocuous to me.)


You may have to edit a bit more to make this work, but it shouldn't require big changes.

One general principle here is that when you have to edit something in a paper, you shouldn't restrict yourself to making only local changes.  Sometimes you can't really fix it without further changes or rearrangement.