Index Match Based on One Date Criteria, Table Contains Beginning Date and End Date

My first post here for assistance.

I have a table in cells A1:C4 as follows:

	A	B	C	D	E
1	Name	ArriveDate	DepartDate		Query Date
2	Smith	10/1/14	10/8/14		10/25/14
3	Black	10/22/14	10/29/14		Name
4	Jones	11/14/14	11/21/14

I've assigned Range Names to each column in the table: Name, ArriveDate and DepartDate

My criteria is the date in cell E2: 10/25/14. I want a formula that would place a name in cell E4 where the ArriveDate is <= 10/25/14 and the DepartDate is >= 10/25/14.

I tried this formula in cell e4:
=(index(Name,Match(1,(value($e$2)>=ArriveDate)*(value($e$2)<=DepartDate),0))

... but it didn't work. (I hit CONTROL + SHIFT + ENTER and the formula went into the cell, but no brackets).

I'm assuming that I cannot use the >= and <=, but I do not know how to accomplish this another way - the data in the table cannot be sorted in order to accommodate a match type.

Any assistance you might provide would be greatly appreciated. Thank you in advance for your help.

Using your formula (but removing an extra () )...
=INDEX(Name,MATCH(1,(VALUE($E$2)>=ArriveDate)*(VALUE($E$2)<=DepartDate),0))
also this...
=INDEX(Name,MATCH(1,(ArriveDate<=E2)*(DepartDate>=E2),0))
ARRAY entered CTRL SHIFT ENTER, gives me an answer of black?

Happy to help and thanks for the feedback