The general names work for LastPass sorting, but can be a bit too vague when mixing into the more detailed grouping and naming in KeePass.
You can also create a password hint that is meaningful to you.
You'll have almost forgotten about LastPass after a few minutes with KeePass.
This is a bit of a double edged sword, as you're now responsible for the safety of said database, but it does mean the data is in your hands.
Authors KeePass Authors for most of it.