Bali appears to be a surname that exists in Hungary and Turkey as well. Some families with this name even seem to be native to Bavaria, Austria and Switzerland since a long time. This coincidence is likely to be accidental. There is also a mystic figure Bali Chakravati in the starting ``book of youth'' Bala Kanda of Valmiki Ramayana. In fact a whole island is named after this Emperor Bali.

According to legend Multan could be the ancient home town of the Balis. I could be distantly related to King Puru of Paurava aka Porus who fought Sikander aka Alexander -326 and was (depending on the source) either a Vaid or a Bali... but then after 100 generations half of humanity can claim this relationship. Bali is of Parashar Gotra (Lord Parashuram was the first Brahmin who took up arms and fought battles). The Balis are one of seven clans that belong to the Mohyal subcaste of Saraswat Brahmins. You can read more about this on semi-fascist webpages like this or politically more correct sites like this or this.

Long ago my branch of the family converted to Sikhism and my great-great-great-great-grandfather Bhai Prem Singh Bali moved around 1819 from Chakwal, situated between Rawalpindi and Jhelum, to Baramulla, Kashmir from where my father migrated to Germany 140 years later. Bhai Prem's ancestors might have come from Mardan. Many other family members have moved to other parts of India, Canada, UK, Australia, USA and elsewhere.

You can also check out the significance of Gunnar and S. if interested.