I'm not familiar with these drugs as I'm a new grad, but did some digging around and got some ideas. I'll be getting into some biochemistry so if this confuses you even more, just ignore this post.
Both norepinephrine and phenylephrine are structurally very similar. You know epinephrine and norepinephrine are biologically occurring hormones. More specifically, norepinephrine is made naturally in the body from an amino acid (tyrosine). On the other hand, phenylephrine is not a naturally-occurring substance but artificially synthesized from benzene. In my head, "Neo-synephrine" almost sounds like "newly-synthesized."
So, I'll remember that Levophed=norepinephrine, which is natural. Then, the other one, phenylephrine is the artificial one and therefore, Neo-synephrine.