All Fediverse platforms let you set a profile name, picture, banner image and short text or biog about yourself. You should see an edit button on your profile page which lets you change all these things.
On Mastodon, there’s also a special feature called Profile metadata which creates a special section of your profile page with clearly labelled website links or any other info you want to highlight about yourself:
To access your profile’s Metadata feature, log in through the website, go to Edit profile > Profile metadata, fill in up to four labels and content, then click Save changes. The labels can be text or emoji, the content can be links, text or emoji. If you do put links in, remember to put the https:// at the start so that they are clickable.
For example, you could have a label saying “My website” and “https://example.com” as the content next to this label. Or you could have a label “Favourite pizza” and a pineapple emoji as the content. It’s totally up to you how you use this feature.
Profile metadata appears as prominent boxes on the website version of Mastodon, and on the official apps it appears in the About section of your profile.
You can verify your identity on the Fediverse by several methods, click here for a tutorial on verifying your account.