Ibn Sina -> Avicenna seems to sound similar though, but I can't speak Latin or Arabic.

At least the cenna and Sina part, you can see they're related. The people Latinizing the name did not just roll a die I presume and had respect for the people who came up with something. It's why algorithm and algebra are both directly from Arabic, algorithm from the guy who wrote this book:

The Concise Book of Calculation by Restoration and Balancing (Arabic: الكتاب المختصر في حساب الجبر والمقابلة, al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah; or Latin: Liber Algebræ et Almucabola)

Al-Jabr

At least in my opinion the Latinization does not seek to hide the fact it's Arabic. In fact, it just takes (directly) untranslatable Arabic terms and puts them into Latin.

It is not certain just what the terms al-jabr and muqabalah mean.

No idea how "Ibn -> Avi" makes sense though, I'd be surprised if it was done with any hostile intent though.