If say, I was to become thane in riften, could I get Iona (the housecarl) to come to my house in Markarth, or anyone of my houses outside Riften, or will they only stay in the house which they're first appointed to. I've checked the wiki, but I have not seen any info regarding this.

No, Housecarl's are forever linked to the city and house where you got them. When you tell them to leave they will ALWAYS go back to there home town.

Thank you. This is what I expected, as I guess it makes sense.

Cheers

Maybe through marriage? You could tell Iona to go live in another (e.g. Markarth)house, I'm guessing she'll return there to wait for you (alone with a male housecarl btw ) when you dismiss her as a follower. Unless of course you're already married to someone else.