The correct term is last night.

"yesterday night" is usually for informal usage. Normally we use "last night".

I would tend to say "last night", "yesterday evening", "yesterday morning", "this morning" and "tomorrow morning". "Last evening" and "yesterday night" may also be heard. These are more a matter of customary usage than a particular rule. When referring to a time today, use "this", as in "this morning", "this afternoon", "this evening". However, when referring to the night yet to come use "tonight", not "this night". "This evening we are going to the symphony", or "Tonight we are going to the symphony."

while the word "yesterday" generally define the recent past (at any given time), I think it is okay to say 'yesterday night' yet, it is rarely used. "last night" is what you would most likely to hear when defining the recent night. "yesterday morning" & "yesterday afternoon" are the right words. I seldom, if not totally, hear "last morning" or "last afternoon". between "today morning" & "this morning", the latter is much used. "tomorrow morning / afternoon / evening" is the standard words used to describe a particular time of the next day. just for an additional info, did you know that "last year" can laso be said as "yesteryear"? I hope this helps :)