But this one I'm sticking to... I tried the "getting to know" version, and have asked that it should be accepted as a correct answer.
It is much less likely here, I have to check some examples or corpus first.
I was only thinking "That girl is getting to know those names" is as likely to appear as a sentence as "That girl is recognising those names" - that is, I think both of them are pretty unlikely! But you can find a context where each of them might just happen. The only one I really think works in English is "That girl recognises those names". But I'm really just happy to be learning, so I'm not going to quibble about it!
The verb is recognizing shoul be changed to recognize or recognizes. The verb recognize is not used in the progressive form.