[name_f]India[/name_f] is fairly popular here in the UK, but it has never sat right with me for the reasons so eloquently explained by @TeaJay above.
[name_f]India[/name_f] is a country which has a long and chequered relationship with [name_m]Britain[/name_m], characterised by inequality, colonialism, and exploitation of [name_f]India[/name_f]’s human, natural, cultural and financial resources by [name_m]Britain[/name_m].
There is a status and power imbalance there which is crucial to all of these kinds of questions. In commonly cited counter-examples, like white British people using [name_u]French[/name_u] or [name_m]German[/name_m] names (so why not X?), there is no such imbalance. But for a white British person to use the name [name_f]India[/name_f], in the context of the power and status imbalances between the two countries, just because it’s “pretty” (or even a bit “exotic”), is a totally different situation.
Of course, I’m sure the parents who have chosen this name haven’t done so with any kind of malicious intent. And many [name_f]Indian[/name_f] people wouldn’t find it in the least bit offensive. But it’s not something that people from outside of a minority group can really deem “OK” or “not OK”.
And it’s always worth examining what it is that we (Brits in particular, in the case of [name_f]India[/name_f]) find so appealing about a particular name. In [name_f]India[/name_f]’s case, I would say that it’s the slightly hippie/bohemian, slightly upper-crusty, slightly “exotic” vibe that is a big factor here, and those three ideas in combination are quite problematic when you examine them like this.
Echoing the thanks to @tianagrace for starting this discussion, and to everyone involved for arguing their points so well and so respectfully.