It is a toponymic surname derived from the lands of Dundemore in Northern Fife, Scotland with origins in the 12th century.
[1] Other spelling variants include Densmore and Dunsmore.
[2] An alternative origin says Dinsmore is a variant of the toponymic surname Dinmore.
[2] Another toponymic surname derivation is based on Dinmore, Herefordshire, England.
[4] Dinsmor is the Welsh toponymic variant that derives from the Welsh and Cornish-British root den- for "fortress" or "fort" and from either the Gaelic root mor- meaning "great", "mighty" or "proud" or the Welsh root mawr- meaning "large" or "warrior", ultimately yielding "a great or large walled city or town" or "a great fortress".