Upvote:3
As @Henry pointed out, the Wikipedia list seems to be copied from other lists that have been around on the internet for some time now. A similar one with more instructive explanations (of where the names came from) is found here. As you can see, it is a colourful mix or historically substantiated names and persons from mythology and literature; it also confuses rulers of the city with (alleged, probably mythological) rulers of all of Phoenicia.
Bronze age king names
Specifically on the bronze age section (the names before those given by Josephus):
Later king names
With regard to the kings in the time after the end of Josephus' list, they are probably a bit better substantiated and (as listed in the annotations of the list mentioned above based on a variety of sources.
A note on ancient names
It is generally hard to identify the exact identity behind let alone the pronunciation of proper names in ancient documents. Take Abi-Milku as an example. We know his name from the El-Amarna letters that were compiled in Akkadian Cuneiform even though this was neither the the native language of the Phoenician author nor that of the Egyptian recipient. Wikipedia lists the full text of letter EA153 in which the name is given (in line 3) as IIa-Bi-LUGAL, LUGAL being the Akkadian Sumerian word for king, indicating the cuneiform character for king, hence presumably read as Melek or Milku (actually MLK) in Phoenician. Or perhaps not, who knows - especially considering that these letters (and a few others) are just about the only written sources we have about Phoenicians of that time.
Note: Pritchard here refers to James B. Pritchard (ed.), Ancient Near Eastern Texts Relating to the Old Testament with Supplement, Princeton Univ. Press, 1969