Approximately eighty percent of Japanese family names are derived from place names. Your second example, Tanaka (field + middle), falls into this category. Most of the others are related to professions. Satō, your first example, is one of these. It's most commonly written 佐藤 (assistant + wisteria). In this case 藤 is not actually used for its actual meaning of wisteria but rather as shorthand for Fujiwara (藤原), the most powerful noble family of the Heian period.

One reason that these may seem strange to someone coming from a Chinese background is that often the Chinese characters used to represent a name were applied to that name after the fact. An example of this would be the name Suzuki. This is most often written as 鈴木 (bell + tree), but it can also be written many other ways such as 寿々木. The word "suzuki" has no connection to these characters other than that their pronunciations match. And sometimes there seems to be no connection whatsoever between a name and the characters used for it. It's not at all rare for a Japanese person visiting an area for the first time to be unable to read some of the place names.

Incidentally, it was only in 1875 that it became mandatory for all Japanese to have last names. Anyone who didn't have one at that point could freely choose one for themselves.