I didn't realize, and am a bit surprised, that a simple surname change has any requirements.... I just don't get how she is legally prevented from making a name change.
Some fathers also associate significance and importance to it!
Some mothers use changing a child's name as a way to hurt their ex and to subtly encourage the child to dissociate from his/her father and identify more exclusively with the mother. That is why one parent should not be allowed to unilaterally change a child's name and should have to jump through some hoops and prove some things, to accomplish it. Because their children have another parent, even if the first parent has come to hate that person.
Let's say a father got custody of his daughter, who had been given the same first name as her mother (his ex-wife); and he concluded he was now so much more important in the daughter's life than her mother was, that he was entitled to change her first name to his mother's? Would you still think, "Why should he be restricted from doing that? He has every right to re-name his kid whatever he wants!"?
In the OP's case, maybe the father will turn out to be so uncaring and uninvolved that it might prove perfectly appropriate to change the child's last name. If so, then as Smithie guessed, he will stop calling after he gets out of rehab, the OP can wait the required length of time, then claim abandonment and get what she wants.
But what if rehab is making him re-think his life and resolve to do better and THAT is why he's calling his child more regularly? She's only 3. He has time to become a better father and she won't even remember that he was worse, when she was 2 (unless her mom constantly reminds her...) What if the OP's current interest in changing her daughter's last name is linked to the fact that her jerk ex suddenly seems more interested in his parental role? What if, subconsciously, the name-change is less about asserting her own importance in the child's life (which is already unmistakeably demonstrated by her raising her daughter, with little or no help from him) and more about asserting that, even if her ex makes the effort to straighten up and fly right, she'd rather keep him on the "worthless, absentee, reject Dad" shelf? Should that sentiment rule the day?
I think these rules are reasonable. If just 3 years ago, she saw fit to name this child after this man - and he's in rehab, trying to clean himself up - he should be given the opportunity the law allows, to show he's going to be involved, before having his name stripped from his child. And again, the OP's not hurt by that. Anyone who knows that child already knows who's raising her, who's influencing her and who is the stable, reliable parent in her life.