I think you should name your class in the way that is most clear of it's usage and you shouldn't care too much if another classes with the same name exist. As you know, the usage of packages reduces the risk of naming collisions.
For any project I think it's good that the whole team should have a convention related to basic naming and formatting used. It's important to use a consistent naming convention so that when new people work on it, they pick it up faster. I think that conventions also help increase productivity since it's easier to remember names.
I think it's good to spend some time thinking about classes, not only in terms of algorithms but also as what business part they fill. To think about why is a class necessary and what brings to the project, can make you more aware of the way your method/class/variable works within the application workflow.
That being said, I think that maybe your IDE has some option to hide some of the classes is shows. I'm using IntelliJ and it has a feature for this situation, even though it's a bit hidden.