There are several possibilities to tie to the most powerful dragon of old In GRR Martin’s world of Ice and Fire.
The Greek, or perhaps Persian hero Bellerophon reinterpreted by the Greeks has the prefix Bel that has been related to destruction in some theories.
Celtic god Belenus related to light, sunlight in particular, possibly its adverse affects in some variations and the slain god Balder also appear to share some of the consonants with each other as well as the Light attributes.
It is just as likely that the name Balerion could be related to the English word “baleful” based on his reputation but even the later word does not in any way contradict the more destructive elements of Sunlight.
Especially since both Apollo, equated with Belenus and his cognate Semitic God Reshef both appear to carry arrows, perhaps reminding of the destructive potential of sunlight equal to its healing powers.
Equally telling is the mention of Balerion naming related to an ancient god of Valyria.
As a conclusion, I would suggest that the name Balerion might be loosely translated as “glaring sunlight.”
If you didn’t hate my little GoT theory, you may find my previous article related to Game of Thrones equally entertaining.