I love [name_m]Lonan[/name_m], such an unfairly neglected name I bet will get popular in the future. Another similar choice is [name_m]Lorcan[/name_m].
One thing I’d say is that [name_m]Matteo[/name_m] (the Italian version as you know) and the much more popular Spanish [name_m]Mateo[/name_m] will both frequently be misspelled, so you might want a middle name with one established spelling. So out go Reed/Reid, Gray/Grey, Rhys/Reese, Ray/Rae, Shay/Shae, even something supremely simple like John/Jon. If your last name is two syllables or more, I’d look for a one syllable middle. If it’s one syllable, a two syllable middle might sounds best.