Argthtjtr

A "standard" definition is something like "cruel," or "remorseless."

But what does this have to do with "ruth" (or lack thereof)? Is this a reference to a kind person named Ruth?

Perhaps a clue may be found from the German Rücksicht, which translates literally into "back sight," or "looking back." Could it then be that a "ruthless" person is actually one who plows ahead, without "looking back" at what the consequences may be?

And how would this evolve into the "standard" definition?

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.

The etymology of ruthless doesn't have much to do with the Biblical Ruth. EtymOnline has:

early 14c., from reuthe "pity, compassion" (late 12c.), formed from reuwen "to rue" (see rue (v.)) on the model of true/truth, etc. Ruthful (early 13c.) has fallen from use since late 17c. except as a deliberate archaism

This does sound similar to the female name "Ruth", but in actuality "Ruth" and "ruthless" probably do not share a root. Again, from EtymOnline:

fem. proper name, biblical ancestor of David, from Heb. Ruth, probably a contraction of reuth "companion, friend, fellow woman."

Ruth is an ancient Hebrew name, whereas reuthe (root of "ruthless") dates back only to the 12th century. It is possible, though I have not found conclusive evidence, that reuthe derives from Ruth--but this does not imply that ruthless directly derives from the name Ruth.

I tend to see the centre of "ruthless" connected with the modern German noun Reue (remorse, regret), "ruth" is a noun with the ending -th as in warmth. We have the verb to rue sth (literary, dated) also in German be-reu-en.

So I would say words like "Rücksicht" or the Bible name Ruth are the wrong track.
"ruthless" means ohne Reue (without remorse).

A pity that etymonline doesn't give the connection to German Reue and bereuen. It would help understand the word ruthless better.

I can also see a connection between reuthe and ruth in the Bible since the Ruth in the Bible showed compassion for her unhappy mother-in-law by staying with her and not deserting her by going back to her own people after her mother-in-law's husband and sons had died.