Tāj al-Mulūk (تاج الملوك) means "crown of kings." It's the kind of name one would not be surprised by. Arabic names and sobriquets are often like that. Royal appellations can take the form "Sword of the Dynasty", "Crown of the Dynasty", "Fighter for the Faith" etc. A friend of mine is named Tāj al-Dīn "Crown of the Faith".
Khārān (خاران) does occur with this individual's name in the Arabic text of the Thousand And One Nights. Or at least, according to Googlebooks it occurs in at
least one of the printed versions Burton would have had access to. Just reading the story though I note that even the Arabic text simply uses the term Tāj al-Mulūk in many references to the guy, which is also pretty normal.
The word Khārān is unknown to me except as a toponym and personal name in Central Asia.. Simply based on the wordshape, it does not sound like a native Arabic word. My gut says Persian. My Persian is not as good as my Arabic, but
Khārān looks on the face of it like it would be a combination of Persian
khār "thorn, goad, prick, horn, sting" plus the plural ending
-ān. I suppose I can see how you would get "amorous blandishments" from that with a lot of squinting. Maybe. My reference volumes, with the rest of my library, are all back in the US, which is not where I am right now. Still, going through the glossaries and lexica available to me, I am drawing a blank. I can't find anything in Steingass' Classical Persian dictionary that really fits any more than that.
Honestly though I would not trust Richard Burton in, well, anything when it comes to his translation of the Thousand And One Nights. Or anything else for that matter. His version is full of bizarre speculations in the footnotes, inexplicable additions, questionable excisions.