Can I ask a stranger girl for her picture to verify?

If a girl that I may have saw but didn't personally know, sends me a message on my phone number or social media account, is it okay to ask her to send her photo or face so I can know who I am talking to?

In one case I had 50-80% idea who she was, the other I had 0-30% idea at first, but then reached up to 60-80%. But still I didn't even know their names. Barely spoke to one, and never spoke to the other.
Is it okay to ask them how they look or send pictures of themselves? Knowing that my picture is there already, so they clearly know who I am.

Also one of them assumed I knew everything about her, as she said: I am (her name). Don't you remember me."
While although I spoke once to her and we had crush on each other, I never knew her name and still don't till today.

Is it weird if I say something like:
[I may know how you look like, but I never knew this name. Can you please introduce yourself].
Because it is annoying that someone suddenly messages you and expects you know who they are.
I say again, I had expectations that she'll contact me (but never expected the way she did), and had an idea as she did (as a stranger, ONLY AFTER 4th/5th message exchange).. but it is stupid to jump to conclusions while I may be totally wrong.

So what is a good way to ask a stranger girl who initiates a conversation online to introduce herself where we just know each other by looks, and she thinks I know her or her name maybe while I almost know absolutely nothing about her?
Can I ask a stranger girl for her picture to verify?
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