Thank you for your question.
Even though your child is under a year old, you must still go through the courts in order to change his last name. It requires the filing of a petition, and notification to the other parent. Here is the basic process:
1) An adult parent or guardian, filing on behalf of a minor (person younger than fourteen (14) years of age), who wishes, for good cause shown, to change the minor's name must file an application in the District Court of the minor's county of residence. Contact the Clerk of Court/District Court in the county where you live -they likely have a petition that you can purchase with the forms if you wish to do this yourself.
2) The Verified Petition includes personal information as required by statute, such as the Adult Petitioner's name, the Minor's Name, the new name that the Petitioner wishes the Minor to adopt and the reasons for the request for change of name.
Filing fees can vary by County, but the Clerk of Court should be able to tell you what the fee is.
3) After filing the Verified Petition and paying the required filing fee for such, the Court will typically assign your case to a judge. Thereafter, you, as Petitioner, will formally request a hearing date to be set (in usually thirty days) by filing the Request for a Hearing. Again, talk to the Clerk of Court when you turn in your petition - they can assist you with setting a hearing.
4) During this interim, the Petitioner must publish a notice of the requested name change. The notice must be published in a newspaper in the county where the Minor resides. The notice is to be published at least once each week for two consecutive weeks. If there is no newspaper published in the county where the Minor resides, then said notice shall be published in a newspaper printed in a county nearest to the residence of the Minor, and having a circulation in the county where the Minor resides.
Direct service must also be provided to all adults who retain legal rights over the Minor (typically the other legal parent if the action is only filed by one parent). If you cannot locate one of these parties, you must be prepared to explain your efforts and the situation to the court.
5) The publication and service requirements must be completed before the court hearing. After publication is complete, you must submit proof of publication to the clerk of the Court. This is accomplished by filing an affidavit, or some proof of publication provided by the newspaper, verifying the publication. The proof should be attached to a copy of the published notice and filed with the clerk. Likewise, Affidavits proving service to each adult served should be attached.
6) At the hearing, the Court may take evidence from all interested parties. The Court may grant or refuse the requested change of name. If the court finds that there is no reasonable objection to the name change, then they will grant the change and sign an order allowing for the name change.