How do I make the player name show up on a /tellraw command? [duplicate]

You'll need to use selectors. These are things like @a, @p, etc. (Look at the link for adding things like scoreboard). To use this in /tellraw, use the following:

"extra":[{"selector":"@p"}]

So, let's say we want a command to say "Hi! My name is ..." Try this:

/tellraw @a {"text":"Hi! My name is ","extra":[{"selector":"@p"}]}

To break it down,

/tellraw @a                    @a means all, so this goes to everyone in the world

{"text":"Hi! My name is ",     The "text" part tells tellraw that the next part 
                               (denoted by :) in quotes is text to be displayed.

"extra":[{"selector":"@p"}]}   The "extra" tag says the next part is something 
                               extra (figures). Then, the "selector" tag says the 
                               next part is a selector, and "@p" means the nearest 
                               player from where the command is being run.

Probably More than You Need to Known, Just Putting it Here Anyways

To tell everyone in the world, use @a. To tell everyone with a score of 3 in the objective Kills, use

@a[score_Kills=3,score_Kills_min=3]

In English, it means "Anybody (@a) with a maximum score of 3 and a minimum score of 3". This may sound weird, but since the only number with a maximum of 3 and a minimum of 3 is, well, 3, that command only targets players with 3 as their Kills score.