Daughter (10) says she wants to be a boy

I would ask why, in case it's being prompted by something that has happened that has made her uncomfortable - and has translated that as meaning she isn't feeling 'like a girl' should.
My DD is a few years older and we've been talking lots about everything recently and she's old enough now to reflect back on some things that she thought when younger, that were simply her not wholly understanding something. At the time I had assumed she understood to a greater degree than she had. I guess what I am trying to say, is children sometimes seem to understand more than they have simply because they didn't yet have that wider perspective and knowledge to see the limits. That comes with time.

Some good responses here OP. The one thing I'd add is not to let this define her. Make sure that she doesn't spend too much online, monitor her internet usage to make sure she's not caught up with any of the dodgy sites / organisations and as others have suggested - listen to her, reassure her and (given the restrictions of lock down) try to make sure she's spending as much time as possible on hobbies, family activities, mum / daughter time etc.
She's very young and puberty is such a shock to girls.

I have no evidence to support his claim that mrs faraday was a great experimental scientist , without whom Michael faraday would not have succeeded

Speaking as a woman who called herself David as a child

Rather than question why, just take every opportunity to show unconditional love, to support her in any thing she does even if it seems strange for a girl. Find ways to make sure she knows about great women and how they have been mistreated

Some things that I remember so clearly are when helping my dad with some car maintenance, when my small girls hand would fit where his wouldn't . First time I had ever been proud to be female

When he was ranting about Rosalind Franklin , Helen Sharman

When he would point out , and so make explicit, everyday sexism

I love rock climbing community as it's a community that respects the physical differences between male and female climbers and dies not treat the female strengths of balance and flexibility as lesser to the male upper body strength and reach

What does she think a boy is that means she can become one? What can a female boy do that a female girl can't? Lot's of listening. It's important to address misconceptions too.

I see "why? What makes you feel this way?" as part of clarifying what "becoming a boy" will mean, the reality being appearance, name, and pronouns, and then asking what differences they expect this will make to their life.

Like Beamur, I think if one of my children came out with this, the first thing I would ask is why? What makes you feel this way?

Is she in the early stages of puberty perhaps and therefore feeling a bit at odds with her body?

Yes many of us might like to be boys sometimes when we think and are told that they have more fun/ power/ protections / money/ status, but we know that nobody can change their sex. I will support you in being the kind of girl and woman who can do all the things that you would like to do but you are valued as the girl you are. If someone is saying or doing something that makes you feel bad about Yourself as a girl, you can share it with me.

If this were me, I'd approach it by asking her why she feels this way and if she wants to make some adjustments, to agree which are ok and which are not. I'd be ok with hair, clothes, we can talk about the name, but no to anything like binding.
As you'll be aware, it's not possible for a child to be prescribed puberty blockers now, so at least you can put that to one side. There are no advantages for girls in taking them anyway.
Keep talking, keep her physically grounded in positive ways to help her self esteem and body confidence in other ways. Reassure her of your love and support and don't trivialise her feelings but also let her understand that self knowledge is a journey, not a destination. If that makes sense.

I'm sure someone will be along in a sec. until they do these people might have some good advice:

www.bayswatersupport.org.uk/