Which (if any) of these name ideas sound native? Which sound foreign?
None of them is good enough.

竭心 is weird.

竭 means to exhaust as in 尽心竭力.

BUT while you can say 尽力, you cannot say 竭心, because you cannot exhaust your heart, while 尽 means to do most/to do to the greatest extent, so uou can say 尽心.

居心 is originally constructed the same as 属意, “to place your heart/mind at”

it cannot stand alone to mean anything:

居心叵测（hard to know where one's heart is placed—— harbouring unfathomable motives）

汝居心正，吾知免矣（《三国志》）（You place your heart upright, (so) I know (I) do not (have to worry about you)—— You are a upright man, ...）

居心 do not mean a tranquil heart or mind Yabla is not always reliable.

When emphasized, 居心 is always a derogatory word:

其人有居心（The man is certainly placing his heart at something—— He is ill intended）

嘉鑫 a mediocre, common name.

酒神 a overly specific name of a foreign deity.

The three bold aspects should all be avoided in a Chinese name.

For example, the name 公明 is good, but no one of surname 赵 will use it as a name.（赵公明 is a deity）