The site and its social accounts point at each other

Search engines work out that an Instagram account, a LinkedIn page and a website are the same organisation partly by the links between them. When they agree, the right accounts can appear beside the site in the results, and a name that is shared with somebody else is easier to tell apart.

It also closes an old gap: a dormant account somebody set up years ago, still first in the results for your name, still showing a logo you stopped using.

Source: Organization structured data and sameAs.

Link from the site to each account (a footer is fine), and from each account's bio back to the site. Then say so in the Organization markup, which is where a search engine reads it rather than guesses:

{
    "@context": "https://schema.org",
    "@type": "Organization",
    "name": "Flour & Co",
    "url": "https://www.flourandco.example",
    "sameAs": [
        "https://www.instagram.com/flourandco",
        "https://www.linkedin.com/company/flourandco"
    ]
}

Tick this when every account you actually use is in that list, and any you don't is closed.