Type your text to get copy-and-paste cursive: script and bold script letters first, then italic styles. Tap one to copy it.
Before you paste it into your name. Because these are different characters, not a font, a screen reader may read each one by its official name (“mathematical bold capital H”), letter by letter, or skip it, and search inside apps usually won’t match it, so people typing your name may not find you. Keep your name, @handle and anything important in plain text, and use styles for decoration. Tap the magnifier on any style to see exactly which characters you’d be pasting.
Script is the curly, calligraphy-style alphabet from Unicode's mathematical letters. A handful of its capitals and lower-case letters (such as ℬ, ℰ, ℋ, ℯ and ℴ) live in an older Unicode block, so they can look slightly different from their neighbours in some fonts; that's normal. Bold script is a heavier version with every letter from one set, so it often looks more even.
Neither script style has its own numbers, so digits stay plain in script and become bold in bold script. If you want something that slants without looking like handwriting, try one of the italic styles further down.
Script is hard to read in long runs and at small sizes. It works best for a name, a short phrase or a heading. Keep your actual @username in plain letters so people can search for it.