Вот так я сумел получить название схемы
using (WdmEntities context = new WdmEntities())
{
//get object models from context
ObjectContext objContext = ((IObjectContextAdapter)context).ObjectContext;
//get all full names types from object model
var fullNameTypes = objContext.MetadataWorkspace.GetItems<EntityType>(DataSpace.OSpace);
///////////////////
var conStr = objContext.Connection.ConnectionString;
var connection = new EntityConnection(conStr);
var workspace = connection.GetMetadataWorkspace();
var entitySets = workspace.GetItems<EntityContainer>(DataSpace.SSpace).First().BaseEntitySets;
for (int i = 0; i < fullNameTypes.Count; i++)
{
Type type = Type.GetType(fullNameTypes[i].FullName);
string schema = entitySets[type.Name].MetadataProperties["Schema"].Value.ToString();
}
}