When creating Item Saved Searches, the Name field displays the parent matrix item name before the matrix child, e.g. Parent Item : Matrix Child.
To display the Child Matrix Item Name only, formula text can be used in the search:
Under Column sub tab of Results tab,
Field: Add Formula (Text)
Formula: Enter case when {parent} is null then {name} else {feedname} end

Now the search displays Child Matrix Item Name.