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Dictionary of Medieval Names
from European Sources

Livia f. Latin Livia, the name of a plebeian Roman gens, of uncertain origin.

The name of two 1st C Roman empresses consort.

While modernly Livia is used as a diminutive of Olivia (cf. Olive), the two names are unrelated to each other.

Italy
Latin
1527 Livia (nom) Rome1527 p. 90
Cite as: S.L. Uckelman. "Livia". In S.L. Uckelman, ed. The Dictionary of Medieval Names from European Sources, Edition 2016, no. 3. http://dmnes.org/2016/3/name/Livia.