What did the night sky look like 100,000 years ago? Question in the title. Would any constellations be identifiable?
(Here I assume by "constellation" you mean "pattern of stars", rather than "region of the sky". To be a pedant one should use "asterism" for a pattern of stars.)

Some asterisms will be recognisable, but there can be some significant proper motion over that period.

Some stars will move more than others. Generally, closer stars will appear to have moved further than more distant stars. So the stars that make up the asterism of "the plough" (which are fairly close) will have moved more, but will still be in the same general region of the sky. On the other hand the bright stars of Orion are more distant. In 100000 years ago the general appearance of Orion would already have formed.

Videos showing 
The past and future of the Plough https://www.youtube.com/watch?v=txJH8RlIoXQ

The future of Orion https://www.youtube.com/watch?v=5KFQD6Bpnm0