Chat prefixes in Minecraft without plugins? [duplicate]

By default, this is impossible, unless you would use a NBT editor, such NBTexplorer.

This technique uses teams, so you will need to create a team. /scoreboard teams (for options press tab)

If you want to look at the file/path on NBT Explorer (it's probably compatable with other programs):

saves\custom world name here\scoreboard.dat\teams\X entries\Prefix

now edit Prefix. This is what you want

If you want color codes, visit the wiki:
Formatting Codes

For example,
§f[§e§lOWNER§f]

Would be <Owner> (when Owner is bold yellow, the rest is plain white)