This is my name. 
Aside from the fact they’re two of the most popular names from the year I was born (1996), they have absolutely no personal meaning for my parents besides they just liked those names. I also don’t think it flows at all. What do you think?
The “a” and the “h” run into each other so the flow isn’t the best. I do love [name]Hannah[/name] and I can’t see this name in any time period because it’s really a classic Biblical name. [name]Jessica[/name] was trendy in the late 1980’s and 1990’s but people often forget that [name]William[/name] [name]Shakespeare[/name] used it in the “Merchant of [name]Venice[/name]”.
I was born in 1993 and [name]Jessica[/name]'s my name too! 
It was the #1 name the year I was born and my middle name’s [name]Marie[/name]. My mom didn’t put any thought into my name, she just said that she liked it. In my opinion [name]Jessica[/name] [name]Hannah[/name] as a combo doesn’t flow too well. I personally don’t like the name [name]Jessica[/name] too much (I’m changing my name), but there’s nothing wrong with it. I like [name]Hannah[/name] a lot more, but I do prefer the [name]Hanna[/name] spelling.
What about [name]Hannah[/name] [name]Jessamine[/name]? I think that works better and the longer mn kind of jazzes [name]Hannah[/name] up.
Popularity aside, nothing is wrong with either [name]Jessica[/name] or [name]Hannah[/name]. The flow isn’t very great as both names end in the same sound, but you could have been saddled with much worse options.
I think it’s cute. I would have liked [name]Hannah[/name] [name]Jessica[/name] more, but that’s only because I think it flows slightly better and I adore [name]Hannah[/name].
I got two names that my parents just really liked; they had no desire to really honor anyone with their first child. And I get where you’re coming from; all my siblings have special names, and mine they just “liked.” Which totally seems unfair, but then I remind myself that these were two names my parents stinkin’ adored, and they thought it was a wonderful, precious gift to give me these two names. It totally makes me appreciate [name]Ashley[/name] [name]Marie[/name] so much more, rhymey, predictable, dated, and boring though my name might be. If you want something different, you could always go by a more unexpected nn, like [name]Annie[/name] or [name]Nan[/name]/[name]Nina[/name] for [name]Hannah[/name], or [name]Essie[/name]/[name]Jessa[/name]/Cess/[name]Cissy[/name]/Sica for [name]Jessica[/name], etc.
But I agree with @misha–a lot of times we just think about how overdone [name]Jessica[/name] was in the past couple decades, but [name]Jessica[/name] was a lovely, charming, captivating Shakespearean heroine–there’s a reason she hung around as long as she did! And [name]Hannah[/name] is a lovely Bible namesake, rather classic, actually, despite its blip on the popularity charts for several years ago.