There is a known issue with your current version of Akeeba Backup and Admin Tools. One of the internal classes has the name Object. This is incompatible with PHP 7.2. We have fixed it over a month ago but there is no released version including this fix yet. The primary reason for that is Joomla! 4 and our mad dash to make our software compatible with it, depriving us from any resources to do anything else at all.
I'd like to point out that PHP 7.2 went stable just days ago. Moreover, this version of the PHP language introduces a lot of significant changes in the language which can affect how existing code works. While we do test our software against new PHP versions -we actually tested Akeeba Backup against PHP 7.2 since the first alpha of PHP 7.2- not all developers do. Even though we will address the issues with a new release it might take months for all Joomla! software to get up to speed with PHP 7.2. For this reason I would very strongly recommend staying on PHP 7.1 for another two months.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!