When checks are attached to a PR the run's title is a separate thing from its name that is visible besides the name on the Conversation tab and in this context it can provide a bit more info.
Some good soul provided this screenshot that shows how the check run's properties map to UI.

Currently the action sets the title to the value of name when output is specified (both of those are properties of output).

The request is to allow to provide title that could be different than name.