Israel does not stamp passports, so no need to "ask." But you'll get an exit stamp from Jordan at the border with Israel, then an entry stamp at your next country after Israel. To anyone who cares enough to examine your passport closely, it will be obvious where you've been.
Lots of discussion as to whether Sudan really does forbid entry to people who've been in Israel. Common wisdom has long said yes, but online descriptions of direct experience have at least sometimes said no.
Hope that's helpful.
Mark
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