namesake: old homestead whose name probably derives from parkán, an obscure word referencing the fence surrounding it
While the Pražský uličník states that no information on the origin of the name could be found, this article from the Prague 5 describes an lecture series featuring people who were up for the task:
Renowned member of the Institute of the Czech Language Dr. Pavel Štěpán also acquainted listeners with an explanation of the name Farkáň. “Everything indicates that the name Farkáň is connected with the word parkán. We are starting from the original meaning of the word, whereas today the term only suggests to us a component of municipal fortification, usually the space between houses and the city wall, or a castle moat,” Pavel Štěpán said as an introduction and continued: “In older forms of Czech, however, the word had a much broader meaning. The origin of the word is important – it comes from the Latin parcanus, which denoted a fence. [...] It is thus most likely that the name of the Radlice homestead Farkáň came from a distinctive fence. [...]”
A scribe may have made a mistake
And how did the present name Farkáň come from the original form Parkán? “The ň at the end undoubtedly came about under the influence of the locative case, which was na Parkáně/Farkáně. [Note: This strikes me as a very weird thing to happen.] The “ň” sound then made its way into the nominative form by analogy. The change from initial P to F can be explained in two different ways: it was either a scribal error—a scribe wrote Farkáň instead of Parkáň and the form caught on (a relatively common occurrence)—or a change due to folk etymology. In the time when the original meaning of the word was no longer so clear, because the word parkán stopped being used with the meaning “fence”, people may have begun to connect the name with the local church property, fara [presbytery],” Pavel Štěpán explained. The name Farkáň, however, is entirely unique; it appears nowhere else. As for the gender of the name, originally it was undoubtedly masculine (see parkán). The locative form “na Farkáně” would not be possible if it were feminine. [Note: This is also a very weird statement. The locative of Farkáň would be Farkáni regardless of gender. In fact, it’s so weird that, along with the other weird claim I pointed out above, it casts into doubt either my own interpretation of the explanation—which seems solid—or the entire explanation itself.] However, it is not impossible that in some cases the gender alternates, even though there would be less alternation among the older residents.
So there you have it, a three-year-old description of a minor lecture that got preserved for exactly this circumstance.