Can I see my own name?
Solution 1:
In-game, by yourself: No. Even if you put down your sign or check the menus, your name will show "correctly".
You can start the game, get the White Soapstone, put up a password and ask a friend to use said password and find your summon sign on an early area, such as the High Wall of Lothric, and then he can tell you how your name shows.
However there are external tools that do the job, such as the Dark Souls 3 Name Check by omgftw. Since the censorship file containing all censored words has been datamined, this checker is updated and accurate.