Here are some baby boy and unisex name suggestions with the middle name Neil or David and the last name Atkinson, aiming for a good flow and sound:

With Middle Name Neil:

• First Name Suggestions: Ethan Neil Atkinson, Owen Neil Atkinson, Liam Neil Atkinson, Caleb Neil Atkinson, Noah Neil Atkinson, Ryan Neil Atkinson, Samuel Neil Atkinson, Elias Neil Atkinson, Arthur Neil Atkinson, Jasper Neil Atkinson. These names offer a blend of classic and modern feels, pairing well with the middle name Neil and the surname Atkinson.

• Considerations: The rhythm and syllable count are important. Names like Ethan, Owen, and Liam create a pleasing flow with "Neil Atkinson," while longer names like Samuel might sound slightly more formal.

With Middle Name David:

• First Name Suggestions: Benjamin David Atkinson, William David Atkinson, James David Atkinson, Alexander David Atkinson, Henry David Atkinson, Charles David Atkinson, Thomas David Atkinson, Daniel David Atkinson, Joseph David Atkinson, Oliver David Atkinson. These names offer a more traditional feel, complementing the classic middle name David.

• Considerations: Similar to the Neil options, consider the syllable count and overall sound. Shorter first names often create a better balance with "David Atkinson."

Unisex Options (suitable for both boys and girls):

• With Middle Name Neil: Avery Neil Atkinson, Riley Neil Atkinson, Casey Neil Atkinson, Jordan Neil Atkinson, Blake Neil Atkinson. These names are gender-neutral and work well with the middle and last names.

• With Middle Name David: Dakota David Atkinson, Eden David Atkinson, River David Atkinson, Skyler David Atkinson, Taylor David Atkinson. These unisex names provide a modern and versatile feel.

This list provides a starting point. The "best" name will ultimately depend on personal preference. Consider saying the full name aloud to assess the flow and sound.