Get over your puffery and credentialism - no one cares.
The degrees at most universities are a bit misnamed. The CompSci degree is an engineering degree, with a focus on writing software to solve problems. If you're building a repeatable process to solve real-world problems, you're an engineer. The few "Computer Engineering" degrees I've seen have been full of project management BS. I really don't understand the choice of name for that. Maybe it will correct in time.
The tiny percentage of people doing academic research work in the field also have CompSci degrees, and it doesn't really seem like you'd need a different undergrad degree program for that yet, as the work you do for your PhD will create the distinction.
Well, I think that you may be correct now, but there are a lot of us with CS degrees that are definitely not engineering degrees in any shape, form, or fashion. My undergrad CS degree (1998) was mostly discrete math. Courses in graph theory, number theory, theory of computation, computational complexity, algorithm design, and symbolic logic comprised most of my curriculum. Understanding why Godel's Theorem put an absolutely road block on computational AI, and why the Church-Turing hypothesis and NP-completeness constrained the types of problems computers could and could not solve were strongly emphasized in my undergrad program. Coding was pretty much optional in most of those classes -- though, tbh, my algorithm professor (Udi Manber, of agrep fame) expressed some surprise and consternation that I had actually passed his course without submitting a single line of compiled code. Out of >60 units in the upper division classes of my CS major, I had exactly 12 units (three 4-unit classes) from the CS catalog that required me to code (compiler design, software engineering, and operating system design and development.) So, no, my CS degree was definitely not an engineering degree. It was about how to ask questions about computation that could be answered in a rational, reproducible way. Engineering, imho, is about taking those rational, reproducible answers and figuring out how to build a money-making widget with them.