What happened to the Muslim Iberians who did not convert during the Spanish Inquisition? Do they identify as Muslim Spaniards?

Can you rephrase the question? The Inquisition had no authority over non-Christians. Once Isabel ordered that all Muslims either convert or be expelled from the realm with a loss of property, most "converted". Still, they would be called Moriscos, not Muslims. In the eastern part of Spain (where Isabel did not have the same level of power that she enjoyed in her own kingdom) many still spoke Arabic and continued to worship the faith freely. In the south, Arabic was not widely used and the newly converted merged cultural practices with Catholic doctrine. It was not until after Isabel was dead and her grandson Carlos I (Charles V) was in power did the kingdom of Aragon pass laws attempting to convert Muslims by force. Local governments and town councils cried foul and even Philip II struggled to deal with their communities. There was a rebellion in the late 1560s between the Christians and Moriscos in the south and thousands were killed and many Moriscos were sold into slavery. Finally Philip III pushed for the expulsion of Moriscos between 1609 and 1614. Roughly 300 thousand people left Iberia under those orders. Without the labor and tax revenue, Spain suffered an economic breakdown and the Morisco Spaniards suffered in exile in North Africa or elsewhere in the Mediterranean world.

I've always liked The Spanish Inquisition: A Historical Revision by Henry Kamen, but there are other studies.