> So for requirements, I wasn't thinking of a list of features, but more like requirements for the outcomes: 'When a customer visits the AirBnB site, they should be able to find and book somewhere to stay within 5 minutes'.
Any requirements are going to be constraints, and may not be reflective of reality, good practices, market needs, user expectations, etc. In your example, discovery and purchase are often not performed in the same transaction/visit/mental process. Different modalities will result in different realistic time constraints. A UX person brought in to come up with "a variety of design concepts" is going to pitch discovery (vacation planning, pinterest-style aspirational ideation, reading travel stories, etc.) as independent from purchase (booking last minute, booking for the future, booking for a specific destination, booking for a specific cost, etc.). If time (efficiency, shorter is better) is a metric they're going to pitch time (time to bounce, longer is better) instead.
Any constraints are going to limit your possibilities, and might result in a local maximum. If you're okay with that, fine, just say it up front, so everyone is on the same page.
UX job titles are pretty varied, because UX roles tend to fill the space left by whatever expertise the product team is missing, whether research, or user contact, or interaction design, or visual design, etc. Again, I think you'd be better served by looking for types of experience.
Designer, UX designer, product designer, UX strategist, all might work as titles. Someone with research experience is probably necessary, but someone that is a dedicated researcher probably won't also be able to do the design work, and someone that specializes in visual design probably won't be able to do the research.
Does that help?