That's actually a really good point, that clan symbols would be more like a badge, not a pattern.
There are a lot of misconceptions about Sakura's family.
Some people have assumed her parents are civilians, but we're shown that they are indeed shinobi, although most likely just chuunin in rank as Sakura mentioned in RTN that they never made jounin. She specifically refers to her mother as a "good-for-nothing-ninja."
I personally don't believe that there is a "Haruno clan", primarily because we've seen no evidence of their existence.
The majority of clans possess a kekkei genkai, Sakura and her parents do not.
Clans are large families, we have not seen any other Haruno family members.
Clans have an infrastructure, hierarchy, customs, other things that make them unique within the world's culture. The only real exception to this are the Uzumaki but there's a reason for this - after Whirlpool's destruction they are scattered. The Haruno family exhibit no such behaviour or adherence to any specific traditions of their line.
Sakura is never introduced as being 'of the Haruno clan' unlike many other characters who hail from one. Just about every person who comes from a clan is specifically stated to be from one (every Uchiha and Hyuuga ever, the Ino-Shika-Chos, the Sarutobis, hell even in Haku's flashback we're told his mom was from a clan.) If Sakura, one of the main characters, was from a clan I believe this would have been stated since Kishi has made a point of doing so for everyone else.
In fact, the only thing to suggest that the Haruno family could be a clan is the circle that Sakura and Mebuki wear on their clothes.
However, as per this post, we have seen that there are shinobi who wear symbols that are not a clan sigil on their clothing. It's entirely feasible that the "Haruno circle" is in fact not a Haruno circle at all and just a fabric pattern. After all, it's such a simple design while most clan emblems are more complex and distinctive, plus Mebuki's dress has several of these circles all over it, so I feel like it could just be for aesthetics.
The circle thing is a theory I could go either way on, however I firmly stand by the belief that the Haruno are not a clan.