If this is him then his mother's maiden name was Thompson. However, I would make the effort to confirm it.
I know of no national service that has access to indexes and death records that no one else does. If any service claims it can find the death certificate it will probably just charge you for something you can do yourself.
In most states the death certificates are controlled by the states' department of health. Some of the records are held by the states' archives. Some have some of their records online and some have partial indexes online. Some states like Pennsylvania, Colorado and thankfully just a few others don't allow access to death records data by the public except by requesting a death certificate.
There are number of states that have indexes online. Some are through the state's department of health, archives, libraries and in the case of a few through Ancestry and other websites. But they all vary in what data they contain and the time periods they cover.
Perhaps Charles went to live with one of his children during the Depression and so he may not have died in Nebraska.