Dear abczyz,
Your husband's logic of having the same name was very correct. If you search the forums you will find people facing problems because of that.
Since, now you got GC, I don't see any problem if you change the name. For changing the name in the passport call the Indian Consulate for your region and they will tell you the procedure. For changing the name in US, there are lot of websites which provides good information e.g.:
http://www.accessnamechange.com/
Also name change forms are specific to state (I don't know if they are specific to county also). Here are some of important FAQs for name change on the internet:
Who can file a petition for name change and where is it filed? Any adult person desirous of changing his name or the name or names of his minor child or children may present a petition to the superior court of the county of his residence, setting forth fully and particularly the reasons why the change is asked, which petition shall be verified by the petitioner.
Is publication of notice required? Yes. Within seven days of the filing of the petition, the petitioner shall cause a notice of the filing, signed by him, to be published in the official legal organ (newspaper) of the county once a week for four weeks. The notice shall contain therein the name of the petitioner, the name of the person whose name is to be changed if different from that of the petitioner, the new name desired, the court in which the petition is pending, the date on which the petition was filed, and the right of any interested or affected party to appear and file objections.
Who must consent to the change of a minor's name? If the petition seeks to change the name of a minor child, the written consent of his parent or parents if they are living and have not abandoned the child, or the written consent of the child's guardian if both parents are dead or have abandoned the child, shall be filed with the petition, except that the written consent of a parent shall not be required if the parent has not contributed to the support of the child for a continuous period of five years or more immediately preceding the filing of the petition.
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Must both parents be notified of a minor's attempted name change? Yes. In all cases, before a minor child's name may be changed, the parent or parents of the child shall be served with a copy of the petition. If the parent or parents reside within this state, service of the petition shall be made in person, except that if the location or address of the parent is unknown, service of the petition on the parent shall be made by publication.
What if one parent resides outside Georgia? If the parent or parents reside outside this state, service of the petition on the parent or parents residing outside this state shall be made by certified mail if the address is known or by publication if the address is not known.
What if one someone objects to the name change? If written objections are filed by any interested or affected party within the applicable time limits the court shall thereupon proceed to hear the matter in chambers.
I don't think this is something for which you need to be stressed about. If you follow the process it is simple to do what you are trying to do.