On Monday, Jack Dorsey, Square’s co-founder and chief executive, announced a way for shoppers to pay by simply giving their name to the merchant. Mr. Dorsey, who also co-founded Twitter, said customers would use a new feature on Square’s iPhone or Android apps, called Card Case, to make payments. Merchants would use one called Register to ring up and track purchases.

Using cellphones to ease offline purchases is a crowded corner of tech investment. Most companies are tackling one aspect of purchasing, like mobile payments or coupons. But Mr. Dorsey is thinking big. He wants Square to be involved in every step of the transaction process by replacing cash registers, loyalty cards and paper receipts. “We think it should be one system,” he said.

The start-up faces formidable competition. Square’s goal is to replace cash registers and point-of-sale terminals and the companies that make them, like Verifone. Square is also taking on the many start-ups that offer cellphone loyalty cards, like Foursquare, and competing with Google, Apple, PayPal and major credit card companies and banks to provide mobile payments.

Square’s new payment services are available at only 50 merchants in New York, San Francisco, Washington, St. Louis and Los Angeles.

Shoppers can use the Card Case app to search for those businesses, pay their bill and store receipts. A shopper opens the app, which looks like a brown leather wallet, clicks to open a tab at a store and then gives the merchant his or her name. The shopper’s credit card number is already stored with Square. Merchants see a photo of the Square user so they can confirm it is the same person.

With the Register feature, merchants can appeal to nearby shoppers who have the Square app by posting deals or menus. They can also store receipts digitally and track customer behavior.

Some shoppers said they were uneasy trusting Square with their credit card information when all it takes to pay is a name, not a plastic card.

According to Square, the photos and the fact that people can only pay if they and their phones are nearby adds a level of protection. For purchases more than $50, shoppers also have to enter a personal identification number as they do at an automated teller machine. Mr. Dorsey compared it to Amazon.com and Apple’s iTunes, which store credit card numbers so people can easily make purchases with their e-mail address and password.

Square joins a host of tech companies, phone carriers, banks and credit card issuers that are trying to replace wallets by letting people use their phones to pay. Most of the efforts are in the early testing stages. Unlike Square, most of the others plan to use a technology called near-field communication, or N.F.C., through which phones communicate information like credit card numbers to the merchants.

Initially, the company most in Square’s sights is Verifone, whose point-of-sale terminals and software are in 70 percent of businesses in the United States. In an interview before Square’s announcement, Doug Bergeron, Verifone’s chief executive, said that Square would not catch on for payments because people will prefer N.F.C. technology and have security concerns about using Square.

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