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Definitions of wary:

adjective:   marked by keen caution and watchful prudence
Example: "They were wary in their movements"

adjective:   openly distrustful and unwilling to confide
name:  A surname (very rare: popularity rank in the U.S.: #41689)

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Alternative Terms
alert observant open-eyed vigilant wakeful watchful wide-awakes awareness-unawareness careful cautious chary circumspect forehanded gingerly prudent wary unwary leery-mistrustful-suspicious-untrusting-wary leery mistrustful suspicious untrusting look-out warily-3 overwary ware-suffix foolhardy headlong closemouthed-2 jealous reckless guardful setanti-joaquin ware guarded