"He doesn't have a computer" 可以说成 "He doesn't own a computer" 或者 "He doesn't possess a computer".

这是英语常用的表达方式，"have" 在这里表示拥有，"own" 也有同样的意思，"possess" 也有同样的意思。

例句：

He doesn't have a computer, so he uses his phone for work.
I don't think he owns a computer, he always borrows mine.
She doesn't possess a computer, so she goes to the pbrary to use one.

翻译：

他没有电脑，所以他用手机工作。
我不认为他有电脑，他总是借我的。
她没有电脑，所以她去图书馆使用。