Some executive hires will push for a fancy title, usually a step grade above what they were before. If they care that much, you should consider that they may not be the right cultural fit for your company. But if you need their skills and they seem like a decent fit, give them just about any title they want because they’ll be happier, which will make them more invested in doing a good job.
But do bicker about it for a bit to appear like you care and that you’re weighing their qualifications.