Ammon is connected to two religions in the US and is used exclusively between the two of them. Prior to the 1960s, Ammon was considered a solely Amish name. In the Amish community, Ammon is bestowed in honor of Jacob Amman, whom the Amish sect is named after.
 
These days. Ammon is also a Mormon name. There are two figures called Ammon in The Book of Mormom, and Utah now has the largest number of babies named Ammon each year.

Ammon

In Egyptian mythology, Amon is a major god associated with creation and the air. He was later fused with the Sun god, Ra, and became Amun-Ra.
 
In the US, Amon is occasionally used as a variation of Ammon, primarily within the Amish and Mormon communities.

Amon

This hyper-rhythmic name has two evocative references. In Greek mythology, she was an island nymph, a daughter of Atlas, who delayed Odysseus from returning home. It is also a genre of West Indian music, originating in Trinidad and Tobago and largely popularized in the States by Harry Belafonte. 
 Calypso was the name of Jacques-Yves Cousteau's research ship--and would make a highly dramatic, musical choice.

Calypso

Chulda 

Darlow 

Elam is the name of no fewer than eight Old Testament figures. The most notable was a grandson of Noah whose followers were dubbed the Elamites. Elam is commonly used in Amish communities today.

Elam

Fjalar

Heidi became known—and popular—via the 1880 eponymous children's classic by Swiss writer Johanna Spyri and, despite decades of American Heidis of all sizes, shapes, and personalities, the name seems permanently tethered to that spunky little girl on the Alpine mountaintop in the book and Shirley Temple movie. 
 The movie was released in 1937, and two years later the name popped onto the charts, and would, a few decades later, be a Top 100 name for close to twenty years. The prominence of Heidi Klum on Project Runway has given it a new recent bump.

Heidi

Heidrun, which is occasionally used in modern Europe, was the name of a mythological goat who nibbled from the tree of life, transforming her milk into mead.  You might think of Heidrun as a cross between Heidi and Gudrun, but there's a good reason this one's never caught on in the US: It's still stuck on that mythical Norse hillside.

Heidrun

Hulda

Hyde, of course, is most familiar as a surname -- as in Mr. Hyde, evil alter ego of Dr. Jeckyll.  Unless Hyde is a family name or you have some other excellent reason for using it, we think you could do better.

Hyde

Hades

Hide

Holda 

Holle 

Huld

Hulra 

Hulta 

Kalypso

In Greek mythology, Lethe was the name of one of the five rivers in Hades, the underworld. Lethe was also the name of the Greek spirit of forgetfulness and oblivion, with whom the river was often identified. 

Lethe

Leofrun

Leto

Liraz 

Loveren 

Pretty sound, provocative meaning, but a little over-the-top. 

Mystery

Mystique

Najwa 

Ortrun 

Name with connotations both mystical and tragic, newly popular in Europe.  For English speakers, though, this name might be ruined by its homonym ruin.

Rune

Rhinedd 

Rhun 

Runa

Runar

Runi 

Ryynari 

Mysterious. In 2016, 13 baby girls in the United States were given this unusual word name -- at least according to the Social Security Administration. We can't help but suspect that some of those baker's dozen had parents who just refused to tell the federal government their daughter's name.

Secret

Secrecy

Sigrun

Tajana 

Velia

Veil 

Whisper

Yamanu

A minor prophet who has his own Book, Zephaniah is another Old Testament gem waiting to be rediscovered now that Noah and Abraham are becoming too trendy. 
 
The vowel-sound ending of Zephaniah is currently bang on trend, along with other Biblical boys' names with softer sounds – think Elijah, Asher and Isaiah. Zephaniah would make a perfect lesser-used alternative to Zachariah.

 A famous namesake is the British writer and dub poet Benjamin Zephaniah.

Zephaniah

Zep 

Zeph 

Vana's list "Names for Privacy Lovers and Secret Keepers" of 49 great name ideas: Ammon - Zeph !

Names for Privacy Lovers and Secret Keepers

Names that mean secret, hidden and concealed