Actually, you know, it kind of makes sense to say that the name is a `Hindu' name. Whether one likes it or not, the label Hindu has no (or rather no ideologically neutral) alternative when used to describe a tradition to which a lot of us belong, whether or not we believe in the tenets of the religion that goes by the same moniker. And, historically, for Indian names, the religious affiliation was very important, and that fact has continued today. Given an Indian name like Shailesh, Ramesh, Nityananda, Harpreet, Riddhi, Salman, Spenta, or Thomas, one can make a very good, though may not be perfect, guess as to the traditional religious affiliation of the community, and similarly, knowing the tradition (and sometimes even the finer social divisions) helps in figuring out the meanings of names. Of course, the regional identity is also very important: names from Bengal, Punjab, Tamil Nadu, Orissa, or Assam do not sound the same!
Most Indian names coming from Sanskrit is technically correct (I haven't actually checked, but it sounds obvious), but this is because we are focussing on the names that belong to the Hindu tradition which in one form of the other would cover about ninety percent of the population, and the sections within it that do use non-Sanskrit origin names are either rural (women in some parts of South India, for example, used Dravidian names of flowers and other natural objects) or underpriviledged and do not appear much in literature that most of us are familiar with, or belong to a somewhat avant garde culture and the names are not thought of as being typically Indian, or the names are thought of as Sanskrit even though they are not (like some Dravidian names of gods etc.) ... I apologize for that long last sentence not making much grammatical sense, but you get what I am trying to say, I hope.
I think further discussion should probably be taken to the lounge unless it sticks clearly to name origins.