I would be thrilled! I'm not a Native English speaker, though neither am I Spanish, so here is that. There is nothing wrong with using anglo-saxon names, but there is also a rising (or continuous) demand for not anglo-centric settings among fantasy readers. So you might actually be at an advantage. Many people these days value cultural representation and diversity and are eager to read about something outside of their cultural bubble. That being said, Spanish-inspired settings are not so rare as you might think.

I might even go further and suggest you not necessarily use "authentic" real names. You can use them, of course, but I suggest you also invent your own names, which do sound Spanish, while not existing in real life. It would make wonders for creating a "Spanish" atmosphere without the pressure of being a "real" Spain and maintain a fantasy feeling to the book. Martin, for example, often uses the existing names, but slightly changed: Eddard (Erward), Joffrey (Jeffrey) etc, alongside with existing (Robert) and absolutely unique (Daenerys). Closer to your setting, in Curse of Chalion (heavily inspired by Spanish history) absolute majority of names are like that: Iselle, Beatriz etc. You can guess which real-world names inspired them, but they still have distinct "fantasy" feeling that makes the setting feel unique instead of secondary.

In my own writing, which is also heavily inspired by my real-world culture, I invent my own names in 90% of situations, which sound similar to the real names but not exactly them. The aim is to preserve the cultural "vibe" but avoid any kind of real-world associations and unintended historical parallels in the mind of a reader so that the plot and writing would speak for themselves, and highlight that my aim is not celebrate my culture, and not to make some kind of historical-political statement.

I hope this helps!