This being the European Middle Ages, the land where people spelled their name however they felt like that particular day (Beutler, Buetler, Beutlerin, Buttler, Bettlerein, Bütler...), it should not come as a surprise that addresses were likewise, shall we say, less than systematic.

A good example might be University of Paris financial records from the 14th century, tracking where some of the students and teachers live. What's not visible from the record itself is that medieval cities were divided into sections (sometimes "quarters," although rarely precisely 4) that had names. Sometimes they might actually be descriptive--a Dyers' Quarter might actually host most of the dyer population, since they needed good water access--but not necessarily.

The most important thing for addresses seems to have been street name. However. Not all addresses have them! Some students' residences are described as "by the gate of [p]" or "next to the monastery of [q]."

And then there's that frustrating bit in Eric Jager's excellent Blood Royal (a.k.a. CSI:Medieval Paris), where he keeps talking about the House of the Virgin Mary and the House of the Shepherds (or whatever; I'm spitballing) and it seems very serious and formal. No, he's basically talking about apartment buildings.

Just like businesses were marked off by symbols (think today's barber's pole or blue-and-green pharmacy cross), non-commercial buildings often had their own name. Surviving examples, and written evidence like the manuscripts Jager used, denote a statue or mold set into a recess in the building's wall. I always think of the Fellowship of the Ring chapter: "At the Sign of the Prancing Pony". (As Middle-Earth is NOT the Middle Ages, however, Tolkien felt and deserved to feel free to give it whatever literacy rates he wanted).

I hope that helps clarify things a little!

To piggyback off of the answer by /u/sunagainstgold - medieval and early modern Middle Eastern cities were also divided into named neighborhoods (usually called محله/mahalla), the number and exact boundaries of which changed over time. As houses lacked specific addresses, someone seeking out a specific building or a specific person would have to resort to asking people for directions, but this was more reliable than it sounds. Neighborhoods were small enough, and communal bonds were tight enough, that any given inhabitant of a neighborhood would likely know of most other inhabitants of the neighborhood, or at the very least would know whom to ask in order to find out. This can be observed in the Sharia court records of the Ottoman period, in which one might find someone's dwelling described as follows: "a house located in Lala Pasha Neighborhood, bounded on two sides by a public road, on one side by the house of Shaykh Muhammad ibn Shaykh Ahmed, on another side by the house of Sinan Ağa," with the expectation that everyone would be familiar with who those people were and where they lived such that they could use them as reference points to spatially orient themselves. Or even more explicitly: "a house in Lala Pasha neighborhood, the boundaries of which are well known."

Street names were quite rare, although if this differs from Europe it may be because the design of Middle Eastern cities often entailed narrow, winding streets not meant for vehicles to be able to pass through (Anatolia partially excepted, wheeled vehicles were almost entirely replaced by animal transport in the Middle East between Late Antiquity and the 19th century). On the other hand, buildings intended for public use could have proper names, including those founded by private persons. For example, I've encountered in 17th-century Ankara both a "Hook Inn" (Çengâl Hânı) and a "Copper Inn" (Bakır Hânı), the latter equipped with "a coffeehouse and sixteen shops." Houses could be described in reference to such buildings, or in reference to other landmarks, natural or otherwise.