Hmm, dunno. If we still call the device that makes labels a “labelmaker” and don’t need a fancier descriptor, seems to be no reason not to just go on calling this doohickey an “aglet maker”.
More properly I suppose it’s an “aglet setter”, as in a grommet setter or snap setter, since its key function is not to actually construct the metal thingy in question but rather to affix it to the textile object that needs it.
[ETA: Appears to be commercially known as “aglet crimping tool”.]
Meanwhile here’s yer Etymology Dictionary info on the word “aglet”:
also aiglet , “metal tag of a lace,” meant to make it easier to thread through the eyelet-holes, but later often ornamental, mid-15c., from Old French aiguillette , diminutive of aiguille “needle,” from Late Latin acucula , an extended form (via diminutive suffix, but not necessarily implying smallness) of Latin acus “a needle” (from PIE root *ak- “be sharp, rise (out) to a point, pierce”)
Figures. Fifteenth century saw a neologism boom in sartorial technical terms, what with Renaissance innovations in buttoning and lacing, curved-seam tailoring, etc.