TOKYO, July 5 (Reuters) - SoftBank"s internet business Z Holdings Corp (4689.T) said on Monday it has agreed to pay Verizon Communications Inc (VZ.N) 178.5 billion yen ($1.61 billion) to secure the rights to Yahoo branding and technology in perpetuity in Japan. In contrast to the retreat of Yahoo in the United States, the brand remains a core part of SoftBank"s domestic internet business where the name adorns a web portal and services like shopping and weather. Verizon is offloading its media businesses including Yahoo and AOL to private equity firm Apollo Global (APO.N) after struggling to compete with internet giants in a $5 billion deal set to close in the second half of this year. Previously known as Yahoo Japan, SoftBank"s internet business rebranded as Z Holdings and is betting on services such as payments app PayPay and chat app Line for growth in Japan and Southeast Asia. ($1 = 110.9800 yen)