The origin of tradition of chanting arjunas name 

                                                                                 during lightning

During the exile prince arjuna visited rishi vedvyas. During the visit when vedavyas asked what arjuna fears most prince arjuna reveals he was afraid of lightning from childhood because he can't predict it when or who it strikes therefore he can't aim a arrow towards it to deflect it. Vedvyas say that he indeed saw the formation of lightning when he was returning from vaikunta he also said he made pradikshnas too it. Then he brings a appartaus with all vayus in glass bowls when he ask arjuna to remove the cork between apparatus restricting stree and purusha vayus the pressure builds up in the glass bowl and the piece of iron in the bowl spins fast and get heated up and transform into a lightning breaking open the glass bowl. Then he teaches arjuna how to control those vayus that are reason for formation of lightning and thunder. After learning the skill from rishi vyas arjuna comes out of the parnashala and invite thunder too fall upon him then he imprisons the thunder in his uthareeyam . When thunder pleads him to realease he makes a condition that whoever invoke  his ten names the thunder shouldn't harm them. Thus the ten names of arjuna i.e.. arjuna phalguna, partha, kireeti, shvethavhana, beebatsa ,krushna, savyasachi, vijaya, dhanunjaya are invoked during lightning and thunder.