I am writing an article about a Phoenician king, Ithobaal I, and was curious about what religion Phoenicians had. Is there any technical term for it or is it just "Phoenician Religion" or "Phoenician Mythology"?
Ancient religions don't generally have technical names, at least not at the civilizational level. Think "Ancient Greek religion", "Ancient Egyptian religion", etc.
Here is a technical article summarizing what little is known about Phoenician religion (as of 1990 anyway). It is aptly titled "Phoenician Religion" and does not offer a general alternative term.