Here are some Irish boy name suggestions using William or Cathal as a middle name:

Using William as the Middle Name:

• First Name Suggestions: Aodhán William, Cormac William, Donnchadh William, Eoghan William, Fionn William, Liam William, Oisín William, Ruairí William, Séamus William.

Using Cathal as the Middle Name:

• First Name Suggestions: Aodhán Cathal, Brian Cathal, Cian Cathal, Conall Cathal, Daire Cathal, Eoin Cathal, Fergal Cathal, Lorcan Cathal, Shane Cathal.

This list provides a variety of options, blending traditional Irish names with the chosen middle names. Consider the sound and flow of the full name when making your final decision. You may also want to research the meanings of the first names to ensure they align with your preferences.