Why is "Melchizedek" translated as a name?

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The Hebrew text translated as "Melchizedek" actually forms a phrase in Hebrew meaning "my king is righteous" or perhaps "my righteous king." Why is it not translated this way instead of as a name?

וּמַלְכִּי־צֶ֨דֶק֙ מֶ֣לֶךְ שָׁלֵ֔ם הֹוצִ֖יא לֶ֣חֶם וָיָ֑יִן וְה֥וּא
כֹהֵ֖ן לְאֵ֥ל עֶלְיֹֽון׃ (Genesis 14:18, Hebrew)

And Melchizedek king of Salem brought forth bread and wine: and he was
the priest of the most high God. (Genesis 14:18, KJV)

"Salem," too, has a meaning, coming from the same root letters as "shalom." So the text might read, if the grammar allows–as it seems it does to me:

"My righteous king, king of peace, brought out bread and wine, and he was the priest of the most high God."

Why are the words converted to names, and how might the translator consistently identify when something should be transliterated as a name rather than translated? (I’m hoping to find an objective, rather than subjective, basis/principle for translation of names–such as grammatical indications.)