That's pretty common in small companies. It's less common in large companies but can happen - you may use the "CTO" title for the founding engineer who still leads code and architecture, then hire someone under a different title (frequently "VP of Engineering") to handle the management / team growing side of the role.

That sounds like a reasonable split to me, so much so I’m not sure I’d understand why you’d want the same person handling both code/architecture and management.