What is the correct linguistic term for names that are statements?

Theophoric names might be what you are looking for:

A theophoric name (from Greek: θεόφορος, theophoros, literally "bearing or carrying a god") embeds the name of a god, both invoking and displaying the protection of that deity. For example, names embedding Apollo, such as Apollonios or Apollodorus, existed in Greek antiquity.

Theophoric personal names, containing the name of a god in whose care the individual is entrusted (or a generic word for god), were also exceedingly common in the ancient Near East and Mesopotamia. Some names of theophoric origin remain common today, such as Theodore (theo-, "god"; -dore, origin of word compound in Greek: doron, "gift"; hence "God's gift"; in Greek: Theodoros) or less recognisably as Jonathan (from Hebrew Yonatan/Yehonatan, meaning "Yahweh has given").

(Wikipedia)