Situation Rosh Chodesh begins on Saturday night. You started se'uda shlishit and continued to eat--including eating at least 1.3 fl. oz. (39 ml, or 1/6 cup) of bread after dark. It is time for birkat ha'mazon.
What To Do Say birkat ha'mazon additions for Shabbat (shir ha'ma'alot, retzei, migdol yeshuot) AND any others for the next day (such as ya'aleh v'yavo for Rosh Chodesh).
Note If you did not eat at least 1.3 fl. oz. (39 ml, or 1/6 cup) of bread after dark, only say the birkat ha'mazon additions for Shabbat.