“Non-rhotic” is to R-droppers as “non-?????” is to L-droppers

It would appear that the word you’re looking for is L-vocalization, which, to quote the wikipedia page on the topic, “is a process by which an [l] sound is replaced by a vowel or semivowel sound”, which appears to be what is being described here, specifically with regards to English L-vocalization — where “an /l/ sound occurring at the end of a word or before a consonant is replaced with the semivowel [w]”, such as the palm/pawm issue (the example given in the article is of milk [mIwk]).

I don’t think there is a term for someone who does this in the non-??? speaker fashion, although L-vocalizer could be a valid construction.

An alternative to LissyNumber's answer is "velarisation" associated with a "dark L". I supposed you could call this a velarising speaker.