Why are names starting with a "J" common, while words starting with a "J" are uncommon?

A lot of the "J" names in English are from the Bible and would have originally been written with an initial I in Latin, as the letter J did not get started until the Renaissance. In modern transliteration of Hebrew these names are written with an initial Y. For example, "Yeʻhoshua" for Joshua, "Yaʻaqov" for Jacob, or "Yirmeyāhū" for Jeremiah/Jeremy/Jerry. The use of /dʒ/ sound in initial uses of I/J comes from Early Old French, through Gallo-Roman influences.

The reason why there are more names than common nouns pronounced this way is that Old English lacks word-initial /dʒ/ and Latin does not have a lot of word-initial I/J followed by a (second) vowel, while Latinized Hebrew has many names starting with I/J. However, some Old French common nouns do start with initial I/J and these properly became pronounced /dʒ/ and spelled with J: for example jeopardy, from jeu parti, or joy from joie.

A further point is that many of these names are essentially the same name. Your list of 18 names:

Jack, Jackie, Jackson, Jill, Janet, Jeremy, Jeremiah, Jake, Jesus, Jacob, Jock, John, Johnny, Jon, Joe, Joel, Janus, Jerr

Broken down into 9 groups:

• John, Johnny, Jon, Jock, Janet
• Jack, Jackie, Jackson ("son of Jack"). Very closely related to John (sometimes treated as a diminutive)
• Jeremy, Jeremiah, Jerr
• Jake, Jacob
• Jill
• Joe
• Joel
• Janus
• Jesus

I suspect these were selected arbitrarily but they illustrate my point well. Other obvious groups include:

• Julian, Jillian, July, etc. -- you've got Jill from this one
• Joseph, Josephine, Jo, etc. -- your Joe
• James, Jim, etc. -- related to Jacob
• Joshua etc.
• Jennifer etc.

Many of these reached English through multiple routes, the most obvious being John/Jacques/Jack, but this group also relates to the initial I/J shift discussed in other answers as demonstrated by Ian/Iain/Ivan (and even Evan for further confusion).

As pointed out in one of the answers above, the commonest names in English are biblical: John/Johan/Jean/Juan, James/Jacob, Joshua/Jesus, Joseph, Judah/Judas, etc., all of which are Hebrew in origin, and begin with the syllable Jah or Yah, meaning "God". There are also common names of Roman or Greek origin, like Julius, Jason, Justin, etc. There are even some names of Germanic origin that begin with J, like Jeffrey.