It can be if it is an anglicized version of the Irish Gaelic Máire or Scottish Gaelic
Màiri. According to Wikipedia it is also a Greek name meaning 'destiny, fate, share'.
Màiri (Scottish Gaelic)
Is Mire a Gaelic name? Bheith ar mire (to be mad, to be in a frenzy); Fear mire (madman); Madra mire(mad dog) (all Irish examples).Perhaps you mean Máire.
One source gives it as Moire.
Moira Deady's birth name is Deady, Moira.
Moira Heath's birth name is Moira Tracey.
Moira Sinise's birth name is Moira Jane Harris.
Moira Shearer's birth name is Moira Shearer King.
Moira Quirk's birth name is Moira Shannon Quirk.
Moira Stuart's birth name is Moira Clare Ruby Stuart.
Moira Anderson's birth name is Mary Anderson.
Moira Orfei's birth name is Miranda Orfei.
Moira Lynd's birth name is Marie-Rosalind Finlayson-Gaud.