深く悔いた or 後悔した

深く悔いた is translated as contrite in English. For example,

The public is often willing to forgive celebrities who are involved in some scandal, as long as they appear contrite.

On the other hand, 後悔した is translated as regretful, and 残念 is translated as sorry.

名称

名称 is appellation in English. Bruce Hoffman wrote

A communist or a revolutionary, for example, would likely readily accept and admit that he is in fact a communist or a revolutionary. Indeed, many would doubtless take particular pride in claiming either of those appellations for themselves.

Those extremists are proud of themselves, and claim responsibility in horrible events, such as Chechen's school siege, and promote their causes. Could Mr. Bush admit his lie on Iraq's WMD and his cheat on Iraq war? He is definitely a brainless extremist. He is utilizing his position to promote his conservative agenda over American lives.