Do I have to acknowledge the company where I started a project when I later publish related research in college?
At least in my field, Acknowledgements are generally regarded a fairly informal mechanism. There are few rules dictating what must and mustn't go in there. However, given that mentions in the acknowledgements don't dilute formal credit, I see no reason not to be as generous, gratuitous and grateful as possible in an acknowledgements section. Its not like adding an author, it costs you nothing and makes you look like a better person. Why wouldn't you?

Also there is probably an argument that you spent time thinking and learning about the general problem domain while being supported by the company.

I recommend adding something like "The author acknowledges BigCorp PLC for first bringing the problem to the authors attention and [financial?] support for work on related approaches", to the acknowledgements.