In September 2020, the company's name of registration changed from Telekom Albania to One Telecommunications, starting the transition to a new brand.

[8] Instructed by Aleksandër Meksi, the team working on it was led by project manager Bashkim Kasa.

[9][10] On 16 January 2019, OTE part of Deutsche Telekom agreed to sell the company, at the time branded as Telekom Albania, for €50 million to Albania Telecom Invest, a company owned by the Bulgarian Vivacom owner Spas Roussev and Albanian-born entrepreneur Elvin Guri.

[11][12] On 10 March 2022, the Albanian Competition Authority approved the sale of ONE Telecommunication in favor of the Hungarian company 4iG.

[13][14] Following their acquisition of the telecommunications operations in Albania, Montenegro and Hungary, 4iG had an agreement to transfer the ownership of these companies to Antenna Hungária raising then its stake at the company to 76%[15][16] The display name of One is One.al, though it might appear on some phones simply as Telekom.al or AMC.

When COSMOTE acquired AMC, the company had 11,000 subscribers actually making outgoing calls.

[citation needed] The company is an official partner to several worldwide used apps, such as AirBnB, Deezer, Evernote, Magisto, etc.

In 2020, One claimed that their 4G network covers the 98.1% of total population, the largest coverage in Albania.

The move sparked strong reactions from consumers who felt that the high price increase across three of the main providers was unfair.