On her husband's first name, an unusual one, Muawiya. Wikipedia says it might mean arm strength, and it's been used by some prominent Umayyad leaders, whatever exactly that means (I'm hazy). [
WP]
The meaning that matters here is the first main one -Islamic dictionary helps (see
here)
Mu'awyiah is one of the most (almost
literally) demonized figures in Shi'a Islam, and is right at the heart of why there's a Sunni/Shi'a split in the first place.
Shi'a Muslims believe that the family of Muhammad,
Ahl al-Bayt (People of the House [of the Prophet]) are the most important figures in Islam.
Only the family of the Prophet has the right to rule over the
ummah, and their beliefs and practices take precedence over the beliefs and practices of any of the other
sahabah (Companions of the Prophet). This stands in contrast with the
Ahl al-Sunnah, the People of Tradition [of the Prophet] and Consensus [of the
ummah] - the followers of
ahadith as transmitted by all the Companions (in other words, Sunni Muslims).
Among the
Ahl al-Bayt, Ali ibn Abi Talib, the cousin and son-in-law of Muhammad (and the first male convert to Islam) is the most important. To the Shi'a, Ali is second only to the Prophet himself, and was the sole rightful successor (
khalif) to the Prophet after his death, supposedly designated as such by Muhammad himself. Ali, however, despite his rightful claim to the position did not become
khalif after Muhammad's death. Abu Bakr was the first
khalif, followed by Umar, and 'Uthman. Through it all, there were a group of Muslims who supported Ali and his right to lead the
ummah. They became known as the
Shi'at Ali, the Party or Partisans of Ali. Hence, of course, the name Shi'a.
In 656, after the assassination of 'Uthman during a revolt, Ali finally became the fourth
khalif. However, despite his exalted position as First Imam and the rightful named heir to Muhammad, not every member of the
ummah supported him or recognized his right to rule - especially because those not of the
Shi'at Ali just saw him as the fourth
khalif, and were not happy with his apparent laxness in cracking down on those who revolted against and killed his predecessor. This rift grew into the First
Fitnah, the civil war that split the
ummah into the Shi'a/Sunni divide of today.
One relative of 'Uthman's, the governor of Syria (!), Mu'awiyah ibn Abu Sufayn (son of the same Abu Sufayn who was Muhammad's greatest persecutor in Mecca, though he later converted to Islam), refused to accept Ali's authority, and full-on war broke out. The war went badly for Ali, with his own supporters splintering and some turning against him in revolts of their own. In 661, Ali himself was assassinated like his predecessor 'Uthman had been, and Mu'awiyah became the first
khalif of the Umayyad dynasty after essentially forcing the abdication and retirement of Ali's son and successor, Hasan.
Mu'awiyah, then, to Shi'a Muslims is a
usurper, against not just Ali, but against Muhammad's authority, since the Prophet named Ali and his family as his true successors. They believe he's a traitorous
kafir who will burn in hell for what he did, and his followers, supporters, and descendants as well for doing things like
starting a tradition in the pulpit of Damascus, Syria (!!), of cursing Ali. Mu'awiyah is the one responsible for taking the rightful rulership of the Imams of
Ahl al-Bayt away from them, and for beginning a millennia and a half of brutal, bloody repression of Shi'a Muslims. He's Oliver Cromwell, Pontius Pilate, Martin Luther, Benedict Arnold, and Vladimir Lenin all rolled into one.
A forum I can't access, acc. to the search, has someone asked to discuss the name saying this back in 2010:
The Shi'a polemical website Answering Ansar says it means "barking bitch".
They really,
really don't like Mu'awiyah.
Same motive according to Rasha Sayed Ali, apparently. She's got them shouting "We took revenge for you, Imam Ali"
But now that the subject is on the table, let's keep in mind that whoever did this, for whatever effect, perhaps this potent name was one factor.
The history to Shi'a Muslims of what Mu'awiyah did, as well as the heavy Syrian connection, make it about as likely for a Syrian convert to Shi'a Islam to be named "Mu'awiyah" as it would be for a convert to Judaism to be named "Torquemada Hitler McBloodlibel."