I also don't think it's a problem. Of course etymology wise it does come from religious side, but that in no way means it somehow a religious thing now. There are many secular and national holidays around the world. For example, commemoration of ending of WW2 is a holiday, but it is not in any way connected to religion. Just like Earth Day or many other. You can of course come up with a better name, but in English it is the most used one (
http://en.wikipedia.org/wiki/Holiday). And I personally don't know another one which could be used.
In other languages of course there are other way to say it. In Latvian we have "brīvdiena" which means "free day" (as in day off). We also have "svētki" which in essence just means "holiday" and it even has a similar etymology ("svēts" means "holy"), but are not considered to have any religious connotations now. For example "Christmas" is "Ziemassvetki" which just means "Winter Holidays" (ziema + svētki). And it was called like that before Christianity, as originally it was a name for a pagan celebration for winter solstice (
http://en.wikipedia.org/wiki/Ziemassvetki).