I prefer [name_m]Fletcher[/name_m] with your surname and in general! But [name_m]Thatcher[/name_m] works too!
[name_f][/name_f]Also like [name_m]Alaric[/name_m], [name_m]Tristan[/name_m], [name_m]Ezra[/name_m], [name_m]Rhett[/name_m] and [name_m]Wilder[/name_m] from your choices 
A few ideas for middles:
[name_f][/name_f][name_m]Fletcher[/name_m] [name_m]Auden[/name_m] Brixey
[name_f][/name_f][name_m]Fletcher[/name_m] [name_m]Callahan[/name_m] Brixey
[name_f][/name_f][name_m]Fletcher[/name_m] [name_m]Jude[/name_m] Brixey
[name_f][/name_f][name_m]Fletcher[/name_m] [name_m]Gabriel[/name_m] Brixey
[name_f][/name_f][name_m]Fletcher[/name_m] [name_m]Axel[/name_m] Brixey
[name_f][/name_f][name_m]Fletcher[/name_m] [name_m]Hudson[/name_m] Brixey
[name_f][/name_f][name_m]Fletcher[/name_m] [name_m]Reid[/name_m] Brixey
[name_f][/name_f][name_m]Fletcher[/name_m] [name_m]Orson[/name_m] Brixey
[name_m]Thatcher[/name_m] [name_m]Miles[/name_m] Brixey
[name_f][/name_f][name_m]Thatcher[/name_m] [name_m]Dean[/name_m] Brixey
[name_f][/name_f][name_m]Thatcher[/name_m] [name_m]Elliott[/name_m] Brixey
[name_f][/name_f][name_m]Thatcher[/name_m] [name_m]Gabriel[/name_m] Brixey
[name_f][/name_f][name_m]Thatcher[/name_m] [name_m]Linus[/name_m] Brixey
[name_f][/name_f][name_m]Thatcher[/name_m] [name_m]Rowan[/name_m] Brixey
[name_f][/name_f][name_m]Thatcher[/name_m] [name_m]Isaiah[/name_m] Brixey
[name_f][/name_f][name_m]Thatcher[/name_m] Olso Brixey