Alyssa and Kevin are looking for a way to honour Alyssa's grandmothers: Ardys and Alice. Alyssa's parents chose her name as a way of honouring them both, and Kevin and Alyssa would like to continue this tradition but are unsure of how best to accomplish this.
The surname is a short 'R' word name. Alyssa writes: "I prefer that the first name we choose not end in "R" or would leave the child sounding like a brand name (India has been ruled out because of this). I prefer longer, lyrical names such as Evangeline, Lydia, and Cecilia. My husband would like a name that is not too clunky or easily made fun of, and also possesses good nickname possibilities."
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What a lovely family tradition! I can see why you would want to continue it. Fortunately, your parents' creativity in creating an honour name, gives you plenty of flexibility.
Ardys + Alice (+ Alyssa):
Your parents found a clever way to honour both grandmothers by combining the letters of both names. Following that same tradition (and possibly borrowing the extra 's' from Alyssa) here are some lovely lyrical names which are made up from the letters in Ardys and Alice:
Ailsa
Adela
Araceli
Ariel / Ariela
Ayla
Carissa
Clarissa
Carys
Cassia
Cerys
Cressida
Elysia
Erica
Isla
Larisa / Larissa
Lydia
Sadie
Sarai
Similar Style: A-'iss':
Besides sharing the same letters, Ardys, Alice and Alyssa all share the pattern of being A names with an 'iss' sound.
Amicia – A popular medieval name, derived from the Latin amicus "friend." While Amicia was the Latin form, most were usally known as Amice (Amis/Amys)
Alexis – From the Greek alexo "to defend," Alexis is a stylish twist on the many Alex- names.
Amaryllis – A pretty and elegant floral name. While on it's own it is stately and elaborate, it has a host of potential nicknames, including Amy, Amari, Mari, Millie, Mally and Ally. Beauty entrepreneur Liz Earle has a daughter named Amaryllis who goes by "Lily".
Anneliese – The pretty German compound of Anna and Elizabeth is found in several forms including Annelise and Annalise.
Anais – A sweet French name ultimately derived from an epithet (Anahita) for Persian goddesses of meaning "pure." The pronunciation (an-eye-EES) isn't intuitive for English-speakers, but the name is well known thanks to the perfume "Anaïs Anaïs".
Alessandra – The flowing and chic Italian form of Alexandra.
Aloisa – A variant spelling of the continental medieval name Eloisa.
Amaris – A rare but pretty choice which coincides with the Latin word amaris "you are loved."
Arista – Both a Latin name meaning "ear of corn" which makes up part of the constellation Virgo, and a feminine form of the Greek Aristos "excellent, best."
Same meanings:
Alice is one of the many descendants of the Old Germanic name Adelheidis meaning "noble sort." Ardys is a little more obscure -- the spelling Ardis was in the top 500 in the USA across the 1920 and 1930s -- and the origin is a bit muddy. The surname form is rare, but it could either be a contraction of the Scottish place-name Allardice, or, more likely, given both were most commonly used in Lancashire in the 19th century, a variant of Arden. Arden (like the Irish Ardal, Welsh Arddun and Celtic goddess Arduinna) is descended from the Proto-Celtic *ardwo "high."
All in all, that gives both Alice "noble sort" and Ardys "high" very complementary meanings. A "noble" is a person of high rank after all. With that in mind, here are some names with complimentary meanings:
Adela, Adelaide, Adeliza/Adelisa, Adalia, Aleida, Adelina, Adeline, Adelina – Like Alice, these are all forms of Adelheidis.
Ailish – The phonetic spelling of the Scottish and Irish form of Alice.
Adara – A Hebrew feminine form of Adar "high, noble, exalted."
Alina – A sleek Arabic name, the feminine form of Ali "lofty, high" and, by extension, "exalted, noble."
Audrey – The vernacular medieval form of the Anglo-Saxon name Æðelþryð (Etheldred) meaning "noble strength."
Arwen – Originally a Welsh name (gwen "white, pure, blessed + ar, an intensifying prefix), Arwen was also used by Tolkien for his elven princess. In his invented language Sindarin in means "noble maiden."
Arya / Aria – Both spellings represent an ancient Sanskrit name meaning "noble."
Bridget – An ancient name borne by a goddess, Bridget means "high" or "exalted one."
Genevieve – It's a bit tentative, but there is strong evidence to suggest that Genevieve is descended from the Common Celtic *geno- and *wesu- "excellent, noble."
Alyssa + Kevin:
Your parents were quite ingenious in combining letters of their mothers' names. Another way that you could continue the tradition might be to combine the letters in both of your names. Here are some combinations using the letters from Alyssa and Kevin:
Avelina
Ainsley
Aliena
Anais
Anika
Eliana
Elysia
Savina
Selena
Sylvia
Valeska
Hopefully, this has been of help. Best wishes with the name hunting!