The rights to a name?

So she’s keeping the name for a hypothetical third daughter 😂 lol, no.

What everyone else said! Out of interest, does she have any DDs already? Because if she does but she decided against using the names for them I'd be raising an eyebrow.

Sophia/Sofia is the most popular name in the world for girls so no one has claim to it!

Isabel/Isabelle/Isobelle etc is also one if the most popular names in the UK over he past 5-10 years so there will be 100s if not 1000s of little girls with this name combination.

She's being ridiculous as she's not even pregnant, but it's a very common name combination so you will meet lots in your wider circle of acquaintances as she grows up

Definitely use the name you love.

Your SIL may never have a daughter! Or if she does she may well have changed her mind on names.

Ridiculous not to use it “just in case”.

Keep the name.
I know of sisters where one picked a name. Loved it. Other sister insisted that it was "hers", had always intended to use it. Basically threw a strop. So it wasnt used.
Obviously a few years down the line, sister had a baby and "changed her mind". Name went unused.

Your DH needs to speak to his sister and tell her that she is being a fucking idiot.

She isn't pregnant, she isn't trying, she may not even have a second DC and if she does it may not be a DD.

She cannot keep a name "just in case" all the stars align at some random point in the future.

No you literally told her what you were planning to call your DD - you are expecting

She told you what she is planning on calling her theoretical DD (and could change her mind - and certainly she wouldn’t worry about you if she did)

Call your child what you want, you can’t “reserve” a name, that’s crackers

The fact she thinks she owns the name and is saying she will use it no matter what would make me even more sure to use the name (which is lovely).
She will look like a right fool if she does have a daughter and uses the same first and very similar second name as you have for your dd. I would dare bet that she won't though- and she knows she would look pathetic.
She simply thinks you are weak and that she can bully you out of using it by laying claim.
Not.A.Chance.
Congratulations on Sophia Isabelle OP.

She wants you to avoid using a name just so that she can have the option of using it, in the event that she gets pregnant and on the 50/50 chance it's a girl?! Tell her where to shove it!

she got a bit arsey and told me that she would be naming their next child that regardless of whether we do or not.

Well, that’s your answer! Given that you’re the one who is actually pregnant and is actually going to be having a girl, I’d stick to my guns. Nobody “owns” a name; she doesn’t and neither do you, even if you use it. (That said, if she does decide to use the exact same name as her brother has chosen, she’s going to look rather odd, but that’s not your problem either!)

Utterly ridiculous. Some of my favourite names were used by close family/friends. They just didn’t go on the list. Do not change it unless there is another name you want more. Never tell anyone in advance of baby’s arrival.

It's a gorgeous name. Use it. She might never get to use it anyway. Honestly don't give it head space and best of luck with the rest of your pregnancy.

Is she normally a bit strange OP?
Even if you’re tempted to change the first name, don’t change the middle name. Isabelle is a family name and nobody knows or cares about middle names except for the parents of the child. Cousins having the same middle names would actually be quite sweet.
In the past when people used a smaller number of names, it was quite normal to have cousins with the same name - Mary, Jane etc. My family tree is full of Sarahs and Johns. No big deal.

First come, first serve

Don't be daft. My sister used a name I had earmarked for DC2 for her DC3. We chose another name. No drama. Just shows you have similar taste in names.
She might not get pregnant, or she might have a boy, and then you would regret not using it.
Never a good idea to reveal a name until the baby is born.

No, don’t back down.. she might never even have a daughter or might change her mind.

The person who has the baby first gets to use the name they want... and the other person gets to chose if they still want to use it when they have their hypothetical baby afterwards.

She should never have asked you not to use it. And you should never have told her your name options in the first place!

Just shrug and say you don't mind the cousins having the same name.

Odds are she won't use it anyway, because clearly them having the same name would bother her. She also might have a boy, or no more kids. Don't let it worry you.

Just be breezy, 'oh we must have similar tastes!' and use it anyway if that's what you decide is your favourite. Especially with the connection to your mum.

Imagine, in 3 years time SIL announces the birth of her new daughter.... Lucy Annabelle. How would you feel NOT using a name over nothing. And as PP says, she might not have another one or might have a boy.

I understand a bit the disappointment. BIL/SIL used a name I had always loved, but I never said anything to them!

I have a friend who went through this exact same scenario. She changed the name to keep the peace. Her sister had another baby a couple of years later and used a totally different name. Claimed she didn't even remember having a conversation about the original name! Use it.

I think you can use the names.

Now, what are these jobs that make you fussier than everyone else?

Use the name.
She's bluffing and probably won't use the exact same name for her future baby.
By the time she gets pregnant, people will raise an eyebrow at her name choice, if she does choose the name, which will probably put her off.

Stick with it.
I was in a similar position to SIL except I was pregnant at the time. I didn't cause an argument about it I said that was the name we are using for a boy so just so they knew in case it bothered them that there might be two. Luckily I found out I was having a girl before their boy was born.

No one has the right to a name so you and SIL can call your child whatever you like. I'm not sure why you should have to change - use the name you love.

Stick with your choice of name . You are currently expecting, she’s not and like others have said , if she does get pregnant, what’s to say it’ll be a girl