There is no need to register your residency in Houston.
The only requirements for expats with visas may be notification of a change of address to the U.S. Citizenship and Immigration Services (USCIS). A permanent resident with a Greencard (alien resident) will need to inform the USCIS via the form AR-11 (http://www.uscis.gov/portal/site/uscis/menuitem.5af9bb95919f35e66f614176543f6d1a/?vgnextoid=c1a94154d7b3d010VgnVCM10000048f3d6a1RCRD&vgnextchannel).