We won't know the answer to this, unless/until we see it happen (again) in a future movie.
As you noted, Days of Future Past changed the timeline; that means everything we saw happening in the first three X-Men movies, plus X-Men Origins: Wolverine, is no longer necessarily true.
In the original timeline, as far as we know, Logan did not know anyone from Xavier's school until he was rescued by Cyclops and Storm. Though there's a strong implication that Xavier knows Logan, none of the other X-Men show any recognition. However, in the new timeline, we already know for sure that's not true -- he met several of the future X-Men, plus Mystique and Magneto, in the 1970's during Days of Future Past.
So, we can be pretty confident that Logan's introduction to the X-Men can't happen the same as it did in X-Men -- at least some of those people in the mansion will know him. It's also likely that he will, at least, remember Jean Gray.
In order to know for sure, we'll have to see it happen again on-screen. We know that Hugh Jackman has agreed to do at least one more X-Men movie, but the rumor is that it's going to be based on Old Man Logan, a story set well into Logan's future, so unless there are flashbacks that's unlikely to help. We also don't know what time frame the next X-Men sequel will be set in, to know if Logan will show up in the X Mansion during that film. Currently the plan seems to be at least 3 more movies (another trilogy), which would likely cover the right time frame, and it would be very surprising if Wolverine wasn't in them, but it's all speculation at this point.