Characters have last names in FFIV, FFV, FFVI, FFVII, FFVIII, FFIX, FFT, and FFTA. Since you determine the names for FFI and FFIII, the question doesn't really apply to those installations. A similar situation exists for FFXI and FFCC, where you can generate your own character(s). The only games with preset first names, but no surnames, are FFII, FFX/X-2, and FFMQ. So, yes, the majority of main characters do have last names.