Long hyphenated surname – what to do when I begin publishing?
As other have commented, the length of your hyphenated surname is not problematic at all: keep it and don't worry.

Fun fact. Uh, well, it took me years to discover that Lennard-Jones was actually just one person and not two, and that the Hanbury-Brown-Twiss experiment was devised by two people and not three, Hanbury Brown (no hyphen) and Twiss. For  Jaynes-Cummings, instead, I tought they were two and they were actually two - amazing! But I would count this as a minor inconvenience, which actually taught me not to make assumptions on surnames (and, as suggested by E.P., this popular page discusses other false assumptions).