TBH any genuine escort who requires a deposit should already have thought about discretion and ought to be suggesting a method of paying without revealing personal details.
That said, paying deposits is a minefield and is not advisable unless you REALLY want to see her and AND are prepared to lose the money. Even if you are correct and it's not a scam, sometimes life happens and the SP may have to cancel, first thought will be that it is a scam and will probably sour any subsequent meeting.