The established primary meaning of the word is an an ethnic slur; this has been so for over a century. Given this, the problem you’re now having was forseeable from the outset.
Your intention in naming your cat “Spik” is irrelevant to the question of whether anyone hearing the name is going to take offence; people hearing the name have no way of divining your intention when you chose it. It’s a good rule of thumb that, if you have to eplain your choice of a word in order to allay any offence at its use, than indicates that it’s an offensive word. This is an offensive word.
How to fix it? You fix it by renaming the cat (maybe to “Span”?). Sure, the cat won’t come any more when you call it, but so what? Most cats don’t come when called, and their owners manage to cope with that.
Or live with the fact that you picked an easily-misunderstood name, that people will continue to tend to misunderstand, and that you will continue to have to explain yourself to them, and some of them will probably not believe you.
sure. this is part abject laziness as citizens of the united states of america is such a mouthful. just kidding. the americans i know love the term but object to being called ‘seppos’ which i don’t but its another slur.
The OED starts out with spiggoty (probably from “[no] speaka da English”) shortened very soon to spig, and then losing the voiced /g/ for the unvoiced c (/k/) in spic. Spiggoty appears around 1910 with both and spig and spic(k) showing up within the next few years.
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As to the OP, “stick” would probably bring the cat, as would sprick, smick, or a host of similar sounds. Cats are not that particular about their names as long as there is a food bowl at the end. (For that matter, how often does one call one’s cat in the hearing of large numbers of people with whom one is not already acquainted? Could this thread just possibly be a bit of a put on?)