One way to look at this is through Kuhn's idea of different scientific phases (parts of the following have already been posted here).
In his book "The Structure of Scientific Revolutions", Thomas Kuhn divides science in to 5 phases:
- The pre-paradigm phase: This is the primordial situation when a given scientific topic was based mostly on competing philosophical speculations. Think physics before Newton or psychology before the 20th century.
- The normal science phase: A specific paradigm (or theory) has been established and now scientists are engaged in confirming and elaborating on the consequences of that theory. Think Physics between the time of Newton and the late 19th century.
- The crisis phase: Experimental results start to seriously contradict the predictions of the theory established in the normal phase. Scientists will try to resolve these contradictions according to established theories. If they fail then science goes into the next phase. Think physics in the 1890-1910 period.
- The revolutionary phase: The previously established paradigm is being abandoned due to too many conflicting experiments and different paradigms and frameworks are competing to establish themselves as the new paradigm. Think of the period between 1910 and 1940 when Quantum Mechanics was being elaborated.
- Post-paradigm shift: Scientists agree on a new paradigm and start work on elaborating it and confirming it, thus returning to phase 2.
It is possible to look at philosophy as being concerned with phase 1 questions: A definitive paradigm hasn't been established, and there are multiple compteing paradigms. So before Newton's theory was confirmed, one had to speak of Aristotelian natural philosophy, Cartesian natural philosophy, Newtonian natural philosophy, etc...each corresponding to a different paradigm, and it was necessary to refer to these theories by the names of the people (or schools) who came up with them.
Then we move to phase 2 (normal science), where a single paradigm is established which everybody agrees on, and we no longer need to mention the name of the person of group of people responsible for the paradigm. Once a paradigm is established, that particular topic branches out of philosophy and becomes its own discipline. Hence people spoke of Natural Philosophy up until the time of Newton, but then started speaking of physics or mechanics after Newton's results were accepted as a dominant paradigm.
So to answer your question: In the pre-paradigm phase there are many competing philosophies (As you put it, it is impossible to determine who is right or wrong) and therefore it is necessary to mention the originators of each idea when discussing them (notice we don't always do that - in phil mind many people speak of physicalism, functionalism, and dualism without referring having to speak of Smart, Putnam or DesCartes all the time). Once a paradigm is established, we've agreed on which philosopher or school of philosophy was right, and then the discipline moves out of philosophy and into its own self contained science, and as a result we no longer need to refer to theories by the name of their authors.
To use your example, we say "the structure of DNA is helical" as opposed to "According to Watson and Crick, the structure of DNA is helical" because the paradigm in molecular biology has already been established, every body agrees that Waston and Crick is the correct interpretation. Compare with quantum mechanics, where there are still competing interpretations and people refer to "Bohmian quantum mechanics", "Copenhagen interpretation" and "Everett-Wheeler Interpretation".
In response to the last paragraph added as an edit (which doesn't seem related to the rest of the question):
Does philosophy have any objective means of proving that famous philosophers are actually better at philosophy than ordinary people and are nor simply idolised because of their notoriety? If it does not, how does philosophy justify it's high-brow status?
Modern philosophy, like sciences, and unlike literature or art, requires that its practitioners train in, learn and then build on a preexisting body of knowledge. In this sense, it justifies it's "high-brow" status in the same way that physics, mathematics (or for that matter classical music) do.