The word for Judaism in the Quran is from the root الهَوْدُ meaning:

التَّوْبَةُ، هادَ يَهُودُ هوْداً وتَهَوَّد: تابَ ورجع إِلى الحق، فهو هائدٌ

It comes from the root Hawdu = repentance; and is related to Tahawwda = to repent and return to the Truth = to become an adherent of the Laws of Moses

إِنَّا هُدْنَـا إِلَيْكَ [7:156]= unto Thee have we turned in repentance!";

the who does it is Ha'id, plaural is Hoodan.

Sadly this has been confused with another word of the same sound Hoodan.