From the name of the patron saint of Zennor, a village in Cornwall, which is of obscure origin. Conceivably it may be derived from the Breton name Azenor or the old Celtic Senovara. According to local legend Saint Senara was originally Princess Azenor of Brest in Lower Brittany, the mother of Saint Budoc. She is also said to have been a mermaid before her conversion (though even after becoming a Christian, "she continued to pine for the sea"). This name was given to 52 girls born in England and Wales in the years 1916-2005.
Frequently used in Sri Lanka as a female given name, a cursory search of social media confirms this fact. Turning to Sanskrit, it looks like the “Sena” part of the name could mean either: "army, missile or dart" with “nara” meaning “human, man”. The soldier, warrior connotations of this meaning for Senara doesn’t sound like an obvious meaning for a girl’s name which is why it is reasonable to surmise that “Sinhala” and “Senara” sounding noticeably similar may account for this name’s isolated popularity in Sri Lanka.