I would like to know what the name of this part is. And also would this part cause running and starting issues.

92 honda accord ex i replaced spark plug wires and one of the wires connected to the part im tryin to identify.

 

That is your ignition coil. Depending on how it fails, you can get no, weak, or intermittent spark to you spark plugs, so it cause running issues.

Before replacing another part, please describe the starting/running issues you are having with your car.

 

running issues and no start issues as well