Applying labels is always fraught and involves compromises. "Islamic World" is well-established and generally recognised. It's also more nuanced than hot takes suggest.
Peter Adamson, host of the History of Philosophy Without Any Gaps podcast and author of the book series from the same project, devotes roughlythe first 20 minutes of his Google Talk about Islamic Philosophy to the matter of why "Islamic World" is in fact the most useful term to use, in contrast to alternatives such as "Arabic" (obviously inapplicable to Persia), "Islam" (fails to acknowledge the role of non-muslim religions, including Christianity, Judaism, Zoroastrianism, etc.).
https://yewtu.be/watch?v=_NKi-XRZ4KI>
As Adamson notes, it would be more accurate to call mediaeval European philosophy "Christian Philosophy" than to call the philosophical tradition of south-Western and south-Central Asia "Islamic Philosophy", as effectively all mediaeval European philosophers were Christian. Adamson also notes that philosophy of the Islamic World draws heavily on Greek and Roman philosophy (largely via the Byzantine empire) as well as Indian and African philosophical traditions.
"Islamic" refers to not merely the religious foundation, but the greater cultural, political, legal (Islamic jurisprudence is a major factor and influence), etc., etc. As with many other contexts, "dominant influence" does not mean "exlusive" or even "majority", but "that which has the greatest overall impact in a specific area". (Cue numerous tedious HN discussions over questions of "monopoly" or geographic applicability of toponyms such as "Silicon Valley" (contrast "Hollywood" or "Bollywood").