It is surprising that so many women whose name is Elizabeth don’t really know the meaning(s) of their name. The Hebrew name is ‘Eli•she•va.’
There is one ‘E•li•she•va’ in the Old Testament:
“And Aaron took him Elisheba, daughter of Amminadab, sister of Nahshon, to wife”
There is another ‘E•li•she•va’ in the New Testament:
“There was in the days of Herod, the king of Judea, a certain priest named Zacharias, of the priestly division of Abijah. He had a wife of the daughters of Aaron, and her name was Elizabeth”
That’s it! One ‘E•li•she•va’ per Testament. Yet the meaning of this name is very Divine. It is made of two parts: ‘Eli’ and ‘She•va.’ The first part means ‘My God’ and the second is the number with the holy attributes: ‘seven.’ In other words, the meaning of the name is “My God of the Seventh’ [perhaps the ‘seventh day.’] Listen to the end of this English name: ‘Sabeth.’ Doesn’t it sound like the Sabbeth day?
‘She•va’ may also mean ‘swear.’ The meaning of the name then is: “(In) My God (I) swear.’
We don’t know for sure which of the two meanings was the original.
We should leave it to each Elizabeth to choose from. Your role may be sharing these meanings with all the “Elizabeths” that you know.