is renaming a factory a feature or can it be?

IE Fission Power Plant Factory 1

+1 from me as well.

My whole base is in factories, and because of that I can't look at the power graph and see what just kicked on and is requiring more power than usual or where I need to focus on efficiency.

+1 from me too, this would be super convenient if it's not too difficult to implement!

Same, that would be an extremely useful addition. I've had many cases where I picked up several factory buildings and then couldn't figure out which one was which in my inventory.

I agree, rename each building is very useful

Is this something that might be possible?

Yeah this would be useful

There is an upgrade you can 'research' that allows you to add icons to factories to label them. That could help