The name is either an abbreviation, in which case the full name can be used, or it is not, in which case the capitalization "Isis" can be used. As the name of the so-called "Islamic State of Iraq and Syria" is usually written with all uppercase, writing your company name with the grammatically correct capitalization might help in distinguishing it.

The name is either an abbreviation, in which case the full name can be used, or it is not, in which case the capitalization "Isis" can be used. As the name of the so-called "Islamic State of Iraq and Syria" is usually written with all uppercase, writing your company name with the grammatically correct more convenient capitalization might help in distinguishing it.