Alternative to Luna?

Selene or Selena.

Celeste
Nova
Leila
Lydia
Wasn't sure if you're looking for a similar sound or a similar meaning!

I love Luna but sadly DP says too many dogs have the name.

How about
Leia
Lila
Aria
Amara
Elena

Loony Luna sadly, I like it too but I’d never use it.
Lyra is too near liar imo.
Una seems to be nearest in sound.
L names:
Lucy
Loveday
Lottie

Moon names
Selene/Selena

Star names:
Stella
Astrid
Seren

I personally think Luna is lovely and think your family would get used to it. It’s a fairly mainstream name now. Its not going to shock anyone in reality.

Similar (ish) names

Cora
Willa
Holly
Aria

I love it but it’s overused by babies and pets.

My friend recently wanted to name her baby Luna but her OH didn’t like it so they went with Leila instead.

Lena
Cara
Hannah
Summer
Melissa
Emily

Eris - is a dwarf plant as well as the Greek goddess of chaos.
One of our cats is called this but would work nicely for a person too!

Cassia
Fern
Etta
Willow
Lenore
Lilah
Cleo
Juno
Aria
Athena
Demi
Lois
Clover
Lexie
Celestia

Surely it has to be Lara?

Lana, Lena, Layla, Leah

Definitely associate it with a cat's name!

How about:-
Lara
Elena (or Eleanor spelling)
Leonie
Kiera
Seren
Sophia

Oh and Layla and Lucy

Lana
Georgia
Kiera

Another vote for Lara or Leia.

Lana or Lara

What about Luana?

Thea.

Lula

Leah

Hmmm maybe not actually, I think Leah was one of Jacob's wives in the old testament... maybe not great for brother and sister!

Lila/Lilah

I think Lucy has a similar sound.
Eden has a similar feel.
My suggestions

Lucia
Selena
Portia