"Last name"・"first name" (on forms usually 性・名) are often translated as "family name"・"given name", because in Japanese the order is reversed, i.e. the family name is given first.
Without being able to read any Japanese, you will not be able to tell which is the first and which is the last name. (You don't know whether 工藤 corresponds to "Taku" or to "Kudo", right?)
jisho.org has a search function for Japanese names (first names, family names, full names), so searching for
工藤 #names gives as first entry
Place, Family or surname
I recommend copy/pasting the Japanese name in the search field as the romanization will not always be recognized correctly. (That is because there exist different romanizations for the same name. Here, 工藤 could also be romanized Kudou or Kudoh.)
Sometimes people write their name as Taku KUDO. If it is in this format, you can assume that the capitalized name is the family name.
Edit. The best rule I can come up with is that in names each Chinese character usually corresponds to at least one syllable (but it may be up to three), so in names like 森 健太郎 Kentaro Mori, you can be pretty sure that 森 is the family name (because it is written first) and it is read Mori (because Mori is very unlikely to correspond to 健太郎).