Arriving in Bangkok at midnight - what date to put for hotel?

I'm arriving in Bangkok at midnight - the trip to the hotel will take another hour. So, I'll be at the hotel at around 1am.

What date should I select for the "check-in" date?

Check in would be for the previous day because that is the night you are staying. You might want to call once you get in to be sure that there is someone there at the desk when you get in or just call to say you are getting in really late that night so that they will expect you.