While in ancient Greece the name "Lindos" was known as the mythological personification of flax, the feminine form, Lindo (not Linda), was rare or non-existent, so any theory tracing our name Linda back to the Greek is non-historical, only pretty guesswork. The fact that names in two cultures or languages sound alike does not mean that they are related, unless you can trace usage. Otherwise, the term "milksop" must surely derive from the obscure Carthaginian name, Milkisop, from the late BC period. Not hardly, when the name is unused for two thousand years, but this is just to show that this "method" of finding meanings or descents of names is bogus.
However, we do know that along about 1830, down where the English-speaking Americans were running into Spanish-Mexican culture, people begin naming their daughters Malinda, the Spanish for "my pretty girl." This is always the earliest spelling.
Only once Malinda began being used back East, after the War Between the States, did Melinda appear as a variant, undoubtedly under the influence of the better known name Melissa (this phenomena of insisting a new name be more like an old familiar one is common). This tended to make the first vowel and the whole first syllable of Melinda even more subordinate to the ending.
In the late 1800's, Melinda crossed over into British usage, never appearing there as the original Malinda. After the turn of the century, US popularity waned. Malinda just about disappeared, while Melinda joined the horde of less well used but still quite acceptable names.
Linda does not appear as a standard name, at its earliest, until about the 1940's, when it suddenly appears as #3 in popularity lists.
It is not reasonable to suppose that the mass of the American population suddenly boned up on the more obscure corners of Greek myth and turned a male personification into a girl's name. Rather, I think this began as "grandparent naming," the common urge to perpetuate one's parents in one's children. In this case, Grandmother's name, Melinda, with its very soft first syllable, was shortened and modernized as Linda.
Linda, brand new and yet echoing tradition at the the same time, caught on with people who didn't have a Melinda in the family. In the 1950's, it was the single most popular name for newborn girls, and has stayed with us since.