Is it permissible for me to use the company's internet for personal and work purposes at home, with the manager's knowledge, if the subscription is registered in an engineer's name to save costs for the company?

The contract concluded between the engineer and the internet provider is valid, and by virtue of it, the engineer has the right to distribute internet lines to a company or others. This is because the internet provider has no relation to what the lessee does with his ownership of the usufructs, unless the contract stipulates that he does not have the right to do so, in which case the contract must be fulfilled. Therefore, what the questioner did by taking an internet connection for personal use and for the company with the company's permission is permissible.