That is left a mystery but it was said before that the people of Ymir share a kind of unity or memory. So owl's saying, 'who's memory is this?' because he has had experience in remembering memories that are not his own. This scene infers that the memory sharing can happen not only for things in the past but also in the future, since it is in the future that Grisha says to Eren, 'If you want to save Armin and Mikasa you have to control this titan power.' The memory could be of either Grisha or Eren.
I think Grisha just named Eren after the owl.
it's more like a prediction/vision than a memory
Hmm... I took it as a memory... I'm not familiar with science fiction but I've seen theories in which future and past exists at the same time, or something like that.
Anyways this is still left a mystery so all we can do is imagine what it means.
This might help:
http://www.mangago.zone/read-manga/shingeki_no_kyojin/mr/manga/shingeki_no_kyojin/vTBD/c088/pg-24/
This and the next page talks about a 'path' that people of Ymir share.
How come owl know about mikasa and armin and mention their name to eren's father even before he met them. And owl name is eren too (⊙…⊙ )