Would the English name "Cody" (pronounced normally, k OH - d ee) be translated into katakana as コーディ or コーディー?
I understand the dash is used to elongate vowels so I'm not sure if the "ee" sound would require it or not.
Both transliterations are fine and natural. You can choose whichever you like unless you are a professional writer and have to follow some opinionated guideline. But I feel I see the elongated version more often in daily life.
When you transliterate Western foreign names, short names usually have a trailing
ー (e.g., ジョー, ハリー, コナー). If the name is three morae long or more without the trailing
ー, then the trailing
ー is often optional (e.g., ケネディ/ケネディー).