She's quite entitled not to give her surname. If she has an unusual one, that could make her traceable outside the store for any nutter. Some way of identifying her within the company (over and above her first name) would have been helpful though.
If goods aren't faulty then, generally, they don't have to refund. Some stores will do this but there isn't a legal requirement.
However, being "unfit for purpose" is an arguable issue IMO. Although they may have been described as "professional", I wonder how reasonable it would be to expect a window cleaner to be climbing them all day every day. After all, it's not the type of ladder that a window cleaner would normally buy. I'm assuming that you wanted to use it all the time rather than just occasional use to a flat roof (i.e. do you use trad or WFP methods?).
The bit to look for is if it's got the kitemark (BS)EN131.
On checking up for info on this though, it seems that the info is rather confusing. Generally though, the BS/EN131 standard should be fine but if it says "light trade" on it, this is probably insufficient as "light trade" is not really for multiple times per day use.
I've looked on the web and there seems to be some conflicting info for this - mainly because European and UK standards are different and there seems to be an attempt to merge the two.
Generally, I wouldn't buy a ladder from B & Q these days. After all, they do supply the domestic DIY market and their ladders just aren't suitable for being climbed maybe 100 times a day.
You might get a better hearing from them if you start talking about credit notes rather than refunds - though I strongly suggest you buy other goods with a credit note if given.
I think you're in a grey area that will need diplomacy rather than confrontation because I'm not convinced that you have a good case.
Sorry if you don't like what I've written but I'm sure you would rather hear an honest view instead of just hearing what you want to hear.