The standard format for naming time zones in the Olson database is Continent / City. The "old" names that you mention as US / Eastern, US / Central and many others are listed as backward compatibility links in the original tzdata distribution (in the back file). According to a comment at the top of the file, these names may have become backward compatibility links in late 1993.
I think that I remember that I read that this standard was adopted because it was considered more stable: geopolitical (country) borders change, cities never move. It is also possible because names such as "East" and "Central" are considered more confusing because they mean different time zones in different parts of the world. However, at the moment I can not find references to the rationale for naming, so do not quote me on this.
Continent / City type names are preferred. Please note that operating systems such as Debian and Ubuntu ask you to select the system time zone using these names (if they do not auto-detect it during installation). Using these names, you, as you say, do not really need to “know which city is TZ,” because the name of the city is, well, part of the name of the time zone! Therefore, if you find out the names of continents / cities instead of or in addition to the names of countries / regions, you are already fine.
Speaking, I do not think that these names will ever disappear. On the time zone mailing list, they are of course always referred to as “backward compatibility” rather than “obsolete” and should remain, despite the fact that PHP recommends.