embedded_svc.settings.extraPrechatFormDetails and embedded_svc.settings.extraPrechatInfo can be used to find Account based on Account Number instead of Name in Salesforce Embedded Service Deployment.

Sample Code:

embedded_svc.settings.extraPrechatFormDetails = [{
	"label": "Account Number",
	"value": "123",
	"displayToAgent": true
}];

embedded_svc.settings.extraPrechatInfo = [{
	"entityFieldMaps": [{
		"doCreate": false,
		"doFind": true,
		"fieldName": "Account_Number__c",
		"isExactMatch": true,
		"label": "Account Number"
	}],
	"entityName": "Account",
	"saveToTranscript": "AccountId"
}];