I came across the name Eschiva while doing research on Melisende, and I find the most intriguing part of this girl's name to be the unusual spelling - it is definitely not a combination of letters you see often. The name has no data in the U.S. In fact, it was rare even in medieval times. Eschiva comes from French esquiver, meaning "evasion." Unfortunately there is very little information on the name itself. However, it is a highly royal name with several namesakes.
One historical namesake is Eschiva de Dampierre, daughter of Eudes III de Dampierre-sur-salon, constable of Jerusalem, and his wife Isabelle of Cyprus. Another was the daughter of Gautier of Beirut (de Baruth), and his wife Agnes. This Eschiva married Jocelin de Gibelet. Another was Eschiva de Montfaucan, widow of Gerard de Montaigu, remarried to Balian of Ibelin. Here is a page that connects Eschiva de Dampierre/Ibelin to Eschiva de Montfaucan. Another historical record of Eschiva of Ibelin, Lady of Beirut, granddaughter of Balian, gives a hint to a nickname - Civa. The text was written in Italian, which would make the pronunciation CHEE-vah. This could give insight to the full name's pronunciation - possibly ess-CHEE-vah, or ess-KEE-vah. The name has also been written Eschive, giving the pronunciation ess-KEEV/ess-KEEV-eh. Balian also had a niece named Eschiva, daughter of Baldwin of Ibelin, and she died before her husband Amalric/Aimery of Lusignan became the King of Cyprus. I am uncertain if she is the same person as Eschiva de Dampierre, but it seems there were three Eschiva de Ibelins. All these women named Eschiva may be of the same family tree, and the name is a very royal one, like the Melisende's of Jerusalem. However, I'm not a historian, so if you're interested in using Eschiva as a baby name, I suggest reading up on the family trees mentioned above. Here is a list with dates and respective titles.
For those of you who read my post on Melusine and the one on Melisende, I will include this family tree on Melusine de Lusignan. You'll see that Eschiva, Melusine and Melisende are mentioned.