But it could be the middle name of the people from the "ancient" kingdom or w.e.
Connection with D and ancient kingdom goes without a doubt.
Roger who knows the true history, talked about D with WB and about some princess (maybe princess of that kingdom). And name of that country is also important considering Gorosei ordered CP/Marines to kill Clover when he wanted to reveal it's name. D is also God's (likely tenryubito's) natural enemy.
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And what exactly is "Dee", slang or what? I googled it and didn't find anything interesting or uninteresting except for surname, given name, river.