Jenny can fruit alone, but it still benefits from a partner. Jenny can fruit on its own, but most kiwi plantings still perform better with another compatible kiwi nearby and other kiwi vines usually need a male pollinizer. It flowers in mid bloom, which is worth knowing if you add a second tree later. Usually grown in USDA zones 7-9.
No single variety stands out as the obvious partner, but that is not a problem here: Matua Male and Tomuri Male all bloom close enough to work. Pick whichever your nursery actually carries. Keep male and fruiting kiwi vines on the same pergola, trellis row, or nearby support so pollinators can move easily between open flowers.
One thing to keep in mind. Most kiwis need at least one male pollinizer for nearby fruiting vines. Jenny is the easier exception, not the rule. Can fruit alone, but another compatible kiwi nearby often improves set and total yield.
To put that into practice: at a minimum, plant one fruiting kiwi plus one compatible male pollinizer, unless you are growing a self-fruitful type such as Jenny. Better still, grow one male kiwi for several fruiting females, or pair a self-fruitful kiwi with another compatible vine for stronger crops. If you have a healthy kiwi vine with flowers but poor fruit set, add a compatible male pollinizer before assuming the vine is the problem.