How do you give people prefixes for their usernames?

Yes, this is possible in vanilla Minecraft but requires the use of a third-party program called NBTExplorer.

First, open the world and add a team for each prefix to be used (e.g. owner, donator, etc). The command is:

/scoreboard teams add [name] [displayname]

Or in your case: /scoreboard teams add owners Owner

Exit the world. Next, download NBTExplorer from here. Open it up.

Select your world within the .minecraft/saves. Navigate to data > scoreboard.dat > data > Teams

Inside that, there should be several 7 entries or 9 entries. Each of these represents a team, open it up and look at the Name and DisplayName entries to tell which is which.

There should be other entries in this: one called Prefix and another called Suffix. Edit the prefix so it says [OWNER] §r MAKE SURE YOU PUT THE SPACE AND COPY-PASTE THE §r! The [OWNER] part can be anything you like though, but for visibility, I recommend [text] so that it is easily told apart from the username. You can also add a suffix if you like which will be displayed after the username.

Press the save button at the top, and reload the world. Join the team with /scoreboard teams join owners [playername] and test it out in chat!

I hope this helps!

Screenshot:

In 1.14, the process described by angussidney is a lot simpler. Use /scoreboard teams add [name] [displayname] to make a team, and then use /team modify [name] [prefix|suffix] "prefix/suffix" to add a prefix or suffix. The /team modify command lets you change lots of other things besides prefixes and suffixes as well.