A chavvy name = a name popular amongst lower socio-econimic classes, people who live on benefits, teenage mums, people who live in social housing, people who wear certain types of sportswear and gold jewellery, etc etc.
Let's call a spade a spade.
There certainly is a distinct cultural identity which runs through the (huge and varied) demographic of people who fall into the categories of i) socially housed ii) young parents iii) poor (or any combination of the above) but certainly does not define all, or any, of those people.
The problem with using a word like 'chav' is that it is almost always used to denote difference and inferiority. People from less afluent or priveliged backgrounds may have a different culture to those from middle class/wealthier backgrounds, but by expressing horror at the thought of being seen to be 'chavvy' you are stating that your culture is better. It's not better, just different.
There will be people who argue that 'chav' doesn't mean the above, but means thieves, or benefit scroungers, or anything else negative. But that's not true is it - the word chav would just as easily be used to describe a working professional if she lived in a council estate and wore gold hoops and a 'mum' necklace.
Snobbery is an ugly thing.
To answer the OP, yes, Kaeden is the type of name popular in a working class culture (ugly term, but there isn't really a better one - but then why should it be uglier than middle class?) but the fact that people might think you are 'chavs' from that fact is very unpleasant. I think you should give that some thought