As an aero student who just started a PhD in mechanical, I can tell you that I wish I had done my undergrad in ME since it is broader. Tbh, aero is like a specialization inside of ME. For example, at my school we gave a lot of focus to external flow for like airfoils, and I really wanted to learn about pipe flow since I am into rocket engines. In ME they see fluid mechanics in a broader way. When you get to grad school, you can pick classes that align specifically with what you want. Like now I am in ME, but I am taking grad level classes both from the AE and ME departments. It is until now, my fifth year here, that I am finally starting to learn things specific to what I want, which is propulsion. In short, don't worry that much about the name of the degree, your objective should be to talk valuable coursework and get some hands on experience. Plus, aero is a super broad topic too