Change in name in passport


My passport contains old name (i.e. name before marriage), while in job, my identity is on new name (i.e. name after marriage), which i changed on the basis of marriage certificate and gazzette copy. I suppose for applying H1B visa i would require to mention new name in the form so as to correlate it with my name in profession. Now, if i want to change the name on passport i am facing one difficulty i.e. my passport has stamp visa of USA as a tourist which i dont want to loose. Need the suggestion for best step to take.

Its ok if old passport has the stamp. You can staple both old and new passports together and carry them both when traveling.

This would be no different from the case when old passport was about to expire and had an active unexpired US visa stamp.