I haven't seen the other thread, but I really wouldn't listen to the voice of Mumsnet. Do a search on the name Eloise, and you will see that for as many people that might think it common, others on Mumsnet have described it as 'posh' and 'pretentious'.
I don't know if you're worrying that it is too common as in popular, in which case that would surprise me greatly, as it has rarely got above 75 in the top 100 names since 1998, although I haven't checked for the past few years, it's certainly not one of the faddy names at the moment.
If you're worried about it being too common in terms of chavvy, then Id say look at some of the famous Eloise's out there:
Countess Eloise - Granddaughter to Queen Beatrix of Holland.
Eloise Taylor - daughter of Lady Helen Taylor, cousin to the Queen and. 37th in line to the throne.
Lady Eloise Anson. Aristocracy.
Finally, if you're still in doubt - do the Telegraph test. Has the name been registered for birth announcements in the Telegraph?? And yes, there's 5 pages of names - including to a lord and lady or two.
Eloise is a name that is ordinary, and used by all classes right from aristocracy down to ordinary folk (like Elizabeth). I don't think it is a name that is put into a particular class.