Looking into this briefly, abandonment is typically an argument to terminate parental rights. Is that what you are attempting to do? Most courts are not keen on doing this unless there is a step parent adoption taking place. This is because if you ever were to go on public assistance, they want to have someone on the hook to go after for reimbursement. Additionally, changing the name to your married name can be viewed as a backdoor adoption, which courts tend to lean away from.
I understand what you are trying to accomplish, and can understand the importance of it to your child. Particularly since his father is absent. Since his rights haven't been terminated, he will have to be notified, and will have the opportunity to object. I have not heard of any means where notification can be skipped altogether just because he is absent. You would be able to present your arguments and he will as well, then the judge would make the decision. Perhaps the judge will allow you to change the name regardless of his objections, but I don't think you will be able to do it without even notifying him.
Also when looking into changing a minors name without consent, was it not helping financially & abandonment, or not helping financially or abandonment. If it was "and" then the fact that he pays child support occasionally could make that an unsatisfied requirement.

