Jane and Carlo are expecting their third child, a brother or a sister to join Luca and Leo. Their surname is long, unwieldy and Italian so Jane prefers a short name that doesn't sound too Italian.
They don't mind using another 'L' name. If it's a girl Jane feels it would be easier to use a different initial, but if it is another boy she feels like they should.
Jack - A family name.
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You have a fantastic list there! All are really lovely choices that sit well next to Luca and Leo. Livia is one of my favourite Italian names and, personally, this seems like the perfect sibset to use it in.
That said, personally, I don't think you need to feel tied to another L name, whether boy or girl. Two L names gets put down to a happy coincidence, three or four L names looks more like a deliberate trend.
Luca and Leo have a sleek Italian vibe that are fashionable, well known and accessible for Brits. If you would prefer not to use another 'L' name, one with a subtle Italian nod would tie the three names in together nicely.
Alessa – The Italian twist on fashionable Alexa with lots of nickname potential.
Marisa – Sophisticated and exotic yet familiar. Marisa is stylish and versatile (with nicknames ranging from Missy and Rissy to Mari and Risa)
Aurea – A lovely Latin name meaning 'golden', spelt Oria in modern Italian.
Pia – A pocket dynamite, packaging sweet charm with exotic flair. Sitting somewhere between Mia and Poppy, Pia is accesible yet unusual.
Rocco – Rocco feels like an all Italian poster-name. Yetr, thanks to its widespread use, its crossed the cultural boundaries as well as Leo and Luca.
Nico – An exotic diminutive for sophisticated and reliable Nicholas.
Santo – An unusual yet striking choice used in Italy.
Violet, Florence, Jude, Eliot and Felix on your list are all fashionable at the moment thanks to their stylish, stately 19th century feel.
Ada – A sweet, mellifluous Victorian belle that has a wonderfully empowering namesake in Ada Lovelace.
Esme – With the lovely meaning of 'beloved', Esme is cute for a little girl and stylish for a woman.
Arlo – A hip rising favourite with Literary and Anglo-Saxon ties. It is short and bold with the fashionable 'o' ending, working perfectly with a complicated Italian surname.
Best of Both:
There are certain names which happily bridge both the sleek Italian and dapper vintage style, giving you the best of both worlds:
Elsa – A name that works in both Italian and English with a sweetly vintage vibe. Yes there is the Frozen association, but fashion-forward parents put Elsa into the top 200 back in 2011 -- long before the film. In a few years the Frozen fever will end, yet Elsa will endure.
Bella – Beautiful Bella has Italian heritage back to the Romans, and a fashionable Victorian favourite with a literary sway.
Beatrice – Beatrice is the quintessential Victorian English lady and yet also dates right back to Renaissance Italy, most famously known for being the name of Dante's love.
Max– Sleek and striking with the cool 'x' ending, Max is derived the mighty Roman Maximus.
Rex – Less common than Max, but still sharing the same bold ingredients is kingly Rex. A strong Latin name given a dapper vintage twist thanks to Hollywood star Rex Harrison.
Ivo – A fashionable, dashing ancient Germanic name used in Italy and once favoured by well-healed British Victorians.
Milo – The Latin form of Miles, in use since the Middle Ages in Britain. Milo sits well next to other Italian names without feeling Italian in and of itself.
If you are inclined to go for another L name, here are some choices which I feel work nicely with Luca and Leo:
Lila – Also found as Lyla and Lilah, Lila was coined by the Victorians as a variant of Leila, a romantic medieval Persian name meaning 'night', which was popularised by Lord Byron in two of his novels.
Lilia – A pretty Latinised form of Lily. Similar Lelia is an Italian name used since the Middle Ages .
Lilac – Much like Violet, Lilac is another purple-hued flower and colour adopted by the Victorians. Purple lilacs were once used to symbolise first love; white lilacs represented purity and youthful innocence.
Lena – A pan-European short form of Helena and Magdelena found in many countries. It became fashionable on its own in Britain in the 19th century. Lena is also a word in Italian meaning "breath" or "energy."
Lysia – Used by the ancient Greeks as an epithet of Artemis, Lysia derives from the Greek lusis "deliverance, freeing." A similar name is the Italian name Licia derived from the ancient region of Lycia, often derived from the Greek lukos "wolf."
Lyra – Taken from the constellation of 'the Lyre', Lyra is both musical and celestial.
Luna – Another astronomical name is Luna, the Roman personification of the moon.
Levi – A stylish Hebrew name borne by one of the founders of the Twelve Tribes of Israel and made fashionable by a hip clothing brand.
Luis – Lewis is a solid British favourite with ancient heritage. Luis (Not uncommon in Britain) gives the same pronunciation with an Italian twist.
Lance – A Germanic name linked with the medieval weapon and its connection to chivalric knights.
Linus – A dapper vintage name, hailing back to the ancient Greeks.
Lewin – Though more recently adopted from the surname, Lewin is in fact a later form of Leofwine, an Anglo-Saxon name meaning "dear friend."
Lex – A short form of stately Alexander used in its own right since the 19th century. In Latin it is also a word meaning "law."
Lowen – A Cornish name meaning "joyful, happy" which gives a different twist to classic Welsh Owen.
I hope there is something of use here. Best of luck!