Jaremy, like Alliser Thorne, were sent to the Wall for being captured Targeryan loyalists. Since the show has not shown either Houe Rykker's coat of arms or House Thorne's, House Targeryen's is used. If the coat of arms for either house is eventually shown, then the House Targaryen's shield will be replaced with their own house's coat of arms.
Basically, the Targaryen shields are shown to help explain why two capable knights ended-up on the Wall versus almost all of the other recruits who end up on the Wall as some sort of punishment or out of desperation.
In regards to Theon and Yara, they have an alliance with House Targaryen to benefit House Greyjoy but both have not pledged allegiance to House Targaryen like Tyrion has. That's why Theon and Yara keep House Greyjoy's shield while Tyrion now has House Targaryen.