After some research and analysis, I'm quite certain that the background colour of your rank, eg. Brown, Navy or Gold has purely got to do with nothing but your XP. If you do check up on the stats of 2 person sharing the same rank but with a different background colour, you'll realise it's their XP that differs greatly.
So here is a breakdown of why your have your respective ranking background colours:
Brown
You lost too much games at once, hence your XP fell dramatically. A brown rank is usually temporary.
Navy
Your XP falls within the average range in respect to your rank. Every average player that plays ranked games will usually have this background colour. It doesn't mean you're doing bad and it has nothing to do with your K/D or W/L ratio. It just means that your XP : Rating ratio is quite balanced.
Gold
Your XP is above average in respect to your rank. You have played many un-ranked games that gained you more XP for your current rank's rating points. XP > Rating points for your ranking's range.
Here is the amount of XP (or more) required for the respective ranks to get a gold background,
4 Stars - 250,000 XP
3 Stars - 200,000 XP
2 Stars - 150,000 XP
1 Star - 125,000 XP
Eagle - 100,000 XP
Silver Cookie - 75,000 XP
As you may have realised, both ranked and non-ranked games gives you XP. But the only difference is, in ranked games you rank up with rating points along with your given XP. So in a way, if you only play ranked games, you hardly get more XP than what you should for that ranking quota. People who plays more games after they get full 4 stars will realise their rank change to gold, since their ratings are maxed out and their XP is the only criteria that increases enough for any change to happen.