"There are other names, once popular, with centuries-deep roots, that truly are about to become extinct," the website explains.
"These 15 names were given to only five babies each in 2013, the lowest number counted by the Social Security Administration.
"Once usage dips below that, they become the dodo birds of baby names."
In particular, those names which have a close connection to religious mythology and culture - for example Alpha, Icarus and Sheba - seem to be proving less and less popular each year.
Indeed, last year, parenting website BabyCenter released its list of Top 100 Baby Names of 2014, suggesting that parents are more inclined to choose a name based on their favorite Netflix shows, rather than looking to the history books for inspiration. .
Obscure baby names such as Garrett and Galina - character names from House of Cards and Orange Is the New Black respectively - are fast-climbing the ranks of popular baby names and a trend which BabyCenter put down to the "Netflix effect".
"This is the year of the binge-watching baby name," said the site's global editor in chief, Linda Murray.
"When you spend 16 hours in one weekend binge-watching your favorite series, you can't help but fall in love with the characters' names."
Nearly 20 per cent of mums surveyed on their naming tactics by the website found inspiration from TV show characters, while 16 per cent looked to actors and actresses for great baby name ideas.
The baby names that are on the brink of extinction
Girls
Alpha: Alpha may be the first letter in the Greek alphabet, but it's one of the last names modern parents consider for their baby girls. Not so in 1880, the first year baby name records were kept in the US, when Alpha was Number 301. It dropped off the Top 1000 in 1944 and is about to disappear for good.
Barbra: Singer Barbra Streisand made her unusually-spelled, condensed name famous in the 1960s, when it peaked at Number 511, only to drop off in the Top 1000 in 1971. Barbara, a Top 10 name for three decades, hangs on in the Top 1000, but Barbra is about to vanish.
Claudine: This feminisation of the ancient Roman name Claudius ranked in the Top 1000 for first half of the 20th century, then blipped to a new height in 1970 on the popularity of singer Claudine Longet, only to fall off the charts in 1975. Claudine along with most other once-popular -ine and -een-ending girls' names are now out of favor.
Nanette: Nanette ranked among the Top 1000 until 77, peaking in 1956. But today, most parents say no to Nanette.
Sheba: Sheba is the short form of the Biblical Bathsheba, disappearing from view with only five baby girls named Sheba in the US in 2013.
Sondra: Sandra's exotic sister Sondra ranked in the Top 1000 from the 1920s through the 80s, peaking in 1939. But the devastating Hurricane Sandy took a lot of wind out of all forms of this name, given to only five girls in 2013.
Thisbe: Thisbe was never ranked in the Top 1000, but this ancient mythological name - she was a doomed young lover whose tale inspired Romeo & Juliet - is about to vanish from the modern lexicon.
Zelma: Zelma nearly broke the Top 200 in 1902 but fell off the list in 1955. Selma, Thelma, and even Velma, might be hanging on by the tips of their antiquated fingernails, but Zelma is about to lose her grip on modern usage.
Boys
Elmo: Just over a century ago, this short form of Guglielmo, the Italian form of William, stood at a respectable Number 247, hanging in there until the 1950s, when it disappeared from view. Any hope of revival was shattered by the ticklish toy from Sesame Street.
Icarus: A dramatic Greek mythological name, Icarus is known for flying too close to the sun with dire consequences. His name has never broken into the national Top 1000, probably due his rash reputation and the icky sound of the first syllable of his name.
Inigo: Inigo is another name that's never ranked here, though it's admired enough on Nameberry to make it Number 261. It's the medieval Spanish version of Ignatius, which has ranked as high as Number 602 on the national list and was used by Cate Blanchett, but Inigo is a no-go.
Llewellyn: A common name in Wales, with the distinctive Welsh double-l beginning, Llewellyn appeared on the US list for six decades, ending in the early 1940s. But despite its rich Welsh history, literary cred and quirky nicknames, Llewelyn seems headed for extinction.
Remus: With his twin brother Romulus, he was a legendary founder of Rome. But the stereotypical image of Uncle Remus, plus the unpleasant first syllable, have kept him permanently off the Top 1000.
Sherwood: The stiff surname Sherwood, which does have the distinguished namesake of influential novelist Sherwood Anderson, managed to make it onto the list from 1897 to 1963, peaking at Number 533 in 1938, Anderson's heyday, but it hasn't been heard from in the 7+ decades since then.
Waldo: Where's Waldo? He's nowhere to be found except on the birth certificates of a scant five boys last year. Waldo actually reached as high as Number 347 in 1881 and remained on the list till 1941, when it became a victim of anti-German sentiment.
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