Square said the new name encompasses its various businesses better than the current name, which is mostly associated with its merchant-payment services. However, the new name also happens to align with Mr. Dorsey’s interest in cryptocurrencies and the technology behind them, called blockchain.
Mr. Dorsey has emerged as one of the highest-profile backers of bitcoin, and to an extent has used Square as a vehicle for that. “I don’t think there’s anything more important in my lifetime to work on,” Mr. Dorsey said at a bitcoin conference earlier this year.