Can I put my finger on what's strange? Use "is recognizing" and it seems she is in a period where she recognizes the names, but didn't before and won't later (which is impossible as apparently the Slavic here is imperfective), or that she can decide whether to recognize them or not at will. I wonder what they mean by using it in the progressive? Perhaps that she "is coming to recognize" or "has been coming to recognize" those names? I think some more context would really help us out here. It's certainly over my head . . .
FWIW, I think the concept of her being in the process of recognizing the names at a particular point in time, while initially/earlier she didn't recognize them, is quite reasonable. But I don't think that interpretation implies that, if she sees the names again in the future, she will no longer recognize them.
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!