Well, yes, this is inherent in having two different words that mean two different things. Obviously pata-leafs and pata-swords are not interchangeable words, but that doesn't mean that one can't originate from the other.
Further supporting the whole patta/leaf thing, just look at the sosun patta, whose name literally translates to lily leaf, a reflection of the shape of the blade. The pata, it would seem, is the same way. A pata blade looks like a patta leaf, so the weapon came to be called a pata. The oldest phonetic spelling of the word, as per the 1860 Tanjore inventory (shown in Elgood Hindu A&R), is "puttah", which is way closer to "patta", clearly showing the transition between the two - or at least that's my take on it
Either way, at least with the sosun patta, it's clear that swords could be given leaf-based names. All I'm arguing is that it's the same with the pattani jamdadu, which shows, in turn, that names can be "customizable" i.e. changed based on the characteristics of the blade/form or the weapon.
Pattani = pata/patta, a long straight blade
Jamdadu = a punch dagger (katar)
Pattani Jamdadu = a punch dagger with a long straight blade
Attached is a silly collage of definitions from Elgood, with the relevant bits highlighted. From Hindu Arms & Ritual and Rajput Arms & Armour, Vol II.