White Lady can fruit alone, but it still benefits from a partner. Most peaches and nectarines can fruit alone, but a second compatible tree often improves fruit set and reliability. It flowers in mid bloom, which is worth knowing if you add a second tree later. Usually grown in USDA zones 5-9.
The good news is you have real choices here. The strongest partners are Saturn and Veteran. Any one of them is enough to get fruit set going. If your nursery has none of those, Halehaven, Belle of Georgia, or Contender will also do the job. If you plant two peaches, keep them close enough for bees to move easily between them. A second peach within about 50 feet is usually plenty in a home garden.
One thing to keep in mind. Chill note: About 800 chill hours. White-fleshed peach. Bloom timing is handled conservatively as mid bloom, so another mid-bloom peach is the safest partner choice.
To put that into practice: at a minimum, one self-fertile peach is enough to get fruit in most home gardens. Better still, plant two peaches or a peach plus a nectarine with overlapping bloom to improve fruit set, fruit size, and spring backup. If you have one self-fertile peach already, add another peach only if you want heavier crops or better odds after erratic spring weather.