How do I make floating tagged text using ArmorStand in Minecraft?

You can't put JSON text formatting in entity names (nor in things like item names/lore). Instead, you should use the section symbol, "§", and a formatting code. E.G: §c before the name for red, §l before the name for bold.

You can't paste or type § directly into chat, though. Instead, you'll need to use a server console (or RCON), or an external tool such as MCEdit or NBTExplorer.

So on Bukkit, you can do & and then put a letter / number to make things colored, but I found this list:

\u00A70 - BLACK
\u00A71 - DARK BLUE
\u00A72 - DARK GREEN
\u00A73 - DARK AQUA
\u00A74 - DARK RED
\u00A75 - DARK PURPLE
\u00A76 - GOLD
\u00A77 - GRAY
\u00A78 - DARK GRAY
\u00A79 - INDIGO
\u00A7a - GREEN
\u00A7b - AQUA
\u00A7c - RED
\u00A7d - PINK
\u00A7e - YELLOW
\u00A7f - WHITE
\u00A7k - Obfuscated
\u00A7l - Bold
\u00A7m - Strikethrough
\u00A7n - Underline
\u00A7o - Italic

Instead of putting & for colors, try these, so say you want the CustomName to be red and bold, use:

\u00A7c\u00A7l

before your text.

WARNING: I have no experience using this in CustomNames, but I did accomplish my message of the day color on my vanilla server using this.