The meaning of ruthless, according to the Oxford English Dictionary, is:
Feeling or showing no pity or compassion; pitiless, unsparing, merciless, remorseless.
The etymology is a thornier issue. For ruthless, the etymology provided is simply "ruth n. + -less suffix." So, we turn to ruth:
The quality of being compassionate; the feeling of sorrow for another; compassion, pity. Also with for.
Its etymology is:
rue v. + -th suffix, perhaps after early Scandinavian (compare Old Icelandic hryggð).
Rue here means:
To affect with sorrow or regret; to distress, grieve. Freq. with it as subject and clause as complement, and without it and with following clause as implicit subject. Now arch.
In the OED, the etymology for this word stretches to—I kid you not—five paragraphs. I'll give you the first of those, which contains most of the important information, I think:
A merging of two distinct but closely related words from the same Germanic base: (i) an Old English strong verb of Class II (hrēowan), cognate with Old Frisian riōwa, riouwa (strong verb; West Frisian rouwe, rouje, weak), Middle Dutch rouwen, rowen, ruwen, rauwen (inflected both strong and weak; Dutch rouwen, weak), Old Saxon hreuwan (strong; Middle Low German rǖwen, rūwen, rouwen, weak), Old High German hriuwan, riuwan (strong; Middle High German riuwen, rūwen, strong, German reuen, weak); and, (ii) an Old English weak verb of Class II (hrēowian), cognate with Old Saxon hriwōn, hrewōn, Old High German hriuwōn, riuwōn; compare also (with different suffixes) Old High German riuwēn (weak Class III), and Old Icelandic hryggva, hryggja (weak Class I); further etymology uncertain: perhaps related to Sanskrit karuṇa pitiable, woeful. The diphthongal West Germanic stem forms do not reflect a Proto-Germanic diphthong, but rather show the result of the operation of Holtzmann's Law (compare the Old Icelandic form); this proves that the conjugation as a strong verb of Class II must be an analogical development in West Germanic. Compare also from the same Germanic base the adjectives Old English hrēow, Old Saxon hriuwi, Old Icelandic hryggr, all in sense ‘sad, sorrowful’.
The following paragraphs are even more technical, dealing with issues like strong and weak verbs in Old English and the decline of the Middle English diphthong ēu. Of particular note: none of them say anything about the name Ruth. Whether ruth and the name Ruth have a shared root I can't say for sure, but it seems to me that the OED's etymology suggests against that hypothesis.