No one can change the name of a child without going through a court process -- should he file a petition to do so you would have to be notified and given the opportunity to contest the name change...the case would go to a hearing before a judge where each of you would state your case and the judge would decide if it would serve the child's interest to change the name to the father's.
From personal experience with just such a case, a family court judge will ONLY change the existing name of a child to the last name of the non-custodial parent (in this case the father) if he found it served the child's best interest - in our case the father was paying support and did maintain semi-regular visitation but was not found to have formed such a significant relationship with our daughter as to warrant a change of her surname to his - meaning that his petition was denied and my daughter still carries my name. The reasoning we were given was that since I was the custodial parent and the one with whom my daughter was most identified it would serve no purpose to give her a last name different than my own after the fact (she was almost a year old at this time).
So, yes he can petition, but the chances of it being granted are unlikely.