A Father wants to name their son "Jeremy" but the Mother is not sure she wants to do that.
The typical noun corresponding to the verb "to agree" is agreement.
If you want to refer to the process of a agreeing however, it's "agreeing" , as in "agreeing to this treaty is not easy".
One is correct. Two is- She talks now mainly of her hometown, Bac-lieu, with it's river and green rice fields.