I think this harp was first published under the name "The Mullagh mast harp" by Joan Rimmer; there is a photo of the harp on p.58 of her book The Irish harp (1969).
The harp is clearly named after a place, but there are four different but similar place names given in the accession register of the National Museum of Ireland.
The harp was purchased in London in 1936, and the Museum paid £65 for it. It is registered in the Art and Industry Division as NMI DF:1944-249. The A&I register says “stated by the vendor to have come originally from Curragh Marsh, Co. Kerry, and that this appeared on an old hand-written gummed labelon the harp...”. Curragh (which just means, a bog) is a townland near Killarney in county Kerry.
The label is still on the harp, and the accession register notes the actual reading of the label, “This harp found in Mulagh Mast, County Kerry”. There is a townland called Maulagh also very near Killarney.
The accession register also notes, “The only Mullamast known in Ireland is in County Kildare” This is the townland of Mullach Maistean.
A marginal pencil annotation in the register reads “Mullaghmarkey in barony of Trughanacmy co. Kerry”. The townland of Mullach Mairce is near to Tralee in County Kerry, and there is still a house there called Mullaghmarky House.
This doesn't really answer the question of where the harp came from, except we can now understand why, as Michael Billinge pointed out years ago, “Mullaghmast” is almost certainly wrong.