Where Discord fonts work and where they don't
Display name: works. This is the name people see above your messages and in the member list, and it accepts Unicode, so a styled display name follows you into every server.
Server nickname: works. A nickname overrides your display name in one server only, which makes it the safest place to try a style before you use it everywhere.
About Me: works, within 190 characters. Styled letters still count toward that limit, so keep the styling to one line.
Channel and role names: work in most cases, and many servers use bold or small caps channel names to group sections. Discord changes text channel names to lowercase with hyphens, so check how the name looks after you save it.
Username: does not work. Usernames are limited to lowercase letters, numbers, periods and underscores.
Messages: work, but markdown is usually the better choice for bold, italic and headings, because markdown is real formatting that screen readers and search handle properly.
Markdown or Unicode: which to use in Discord messages
Discord formats messages with markdown. Wrap words in two asterisks for **bold**, one for *italic*, two underscores for __underline__ and two tildes for ~~strikethrough~~. Start a line with #, ## or ### for a heading, and with -# for small grey subtext. Backticks make `code`, and two vertical bars hide a ||spoiler||.
Markdown is the better choice for messages: it is searchable, readable by screen readers and costs no extra characters. Unicode styles are for everything markdown cannot reach, mainly your name, nickname and About Me, and for looks markdown has no syntax for, such as script, small caps or upside-down text.
If you want both, type your message here, copy the markdown version from the box under the styles, and send it as is.
Picking a style for a Discord name
Discord names are read in a busy member list at a small size, so legibility matters more than in a bio. Bold and bold italic stay readable at that size. Script, fraktur and squared letters look good in a screenshot but are hard to read in a list of 200 members.
A common pattern is to keep part of the name plain, for example a styled first word and a plain second word, so people can still type enough of it to @mention you. If you moderate a server, keep your own nickname plain so members can find you when they need help.