I think it would be great if the Saints would move to San Antonio. Personally, I believe the people of San Antonio would embrace the Saints & support them more so than NOLA.
New Orleans can keep the Saints' name - San Antonio can come up with a better name.
How 'bout the San Antonio Toros?
How about the Bandidos, really un-PC.
The Saints fans have supported them for 40 years even when the team hasn't produced much reason to be a fan. There's no better fan base than the NOLA and Gulf Coast fans.