I did the quest to end the skooma trade including going to the gambler den cave. Went back and talked to the jarl and completed the quest.. The option to become thane wasn't even a topic I could choose from. So my question is: is becoming a thane for the rift bugged?? Or do I just need to do quests for citizens of the rift and then I will be able to become thane?

Become more knows...so yeah do quests in riften. Go talk to svana in the bunkhouse, the balding guy in the inn, ingun blackbriar in the alchemy shop, the blacksmith, brandshei the dark elf, the argonian male in the inn, and the argonian jeweler

Yes, do some quests for the people of Riften and you'll be fine.

It can be glitched easily though just so you know.....

In my experience it can glitch, altho I'm not sure exactly how it happens. With one of my PCs I did all the skooma trade quests and had already completed 5/5 tasks for the people of the Rift. I got the option to buy the house which I did but the dialogue option for initiating the process of becoming Thane just never came up, no matter how many times I went back to talk to the Jarl. I would go out and do even more tasks in the Rift but nothing seemed to work. Finally I just consoled it in and got my title and ceremonial weapon because I couldn't figure out how else to make it happen.

Haven't even touched Riften with regard to the Thane stuff in my current playthrough and I'm not touching it until I finish the CW quests because I suspect the glitch may have something to do with the fact that the position of Jarl can go from one person to another and back again depending on how you play out the war and whether or not you do Season Unending to finish out the MQ first.

The glitch used to be (not sure if it is still glitched) that if you visit Honeyside after you purchase it, but before becoming Thane, you cannot become Thane. One of the things that can throw you off is that you will be directed to visit your house first, but it's best to just speak to the Jarl.

That may have been what happened to me, then. I'll have to remember that tip this time around.