Pickering can fruit alone, but it still benefits from a partner. Most mangoes can fruit with their own pollen, but another mango nearby often improves fruit set, fruit size, and reliability when bloom weather is uneven. It flowers in mid bloom, which is worth knowing if you add a second tree later. Usually grown in USDA zones 9-11.
The good news is you have real choices here. The strongest partners are Alphonso, Ataulfo / Honey, Carrie, Cogshall, and Glenn. There are 4 more in the full list below. Any one of them is enough to get fruit set going. If your nursery has none of those, Kent, Manila, or Valencia Pride will also do the job. Keep mango partners close enough for bees and other blossom visitors to move easily between trees. In container or greenhouse plantings, even a second tree nearby can help when bloom weather is uneven.
One thing to keep in mind. Most named mangoes can fruit on their own, but a second mango nearby can still improve fruit set and crop consistency in warm climates. Mangoes are only dependable outdoors in frost-free or near-frost-free climates. In cooler zones they usually need a container, greenhouse, or winter protection. Chill note: No chill requirement. Compact mango often recommended for containers or small protected patios. In zone 9 it still usually needs winter protection.
To put that into practice: at a minimum, one named mango can fruit in a warm enough climate, protected greenhouse, or large container setup. Better still, plant two mango cultivars with overlapping bloom if your climate supports them, especially if you want steadier crops and better fruit set during erratic bloom weather. If you garden outside frost-free conditions, solve winter protection and heat first. A second mango helps, but climate fit matters more than adding another cultivar.