I'm glad you have researched this out. But people who have not studied Koine Greek, or for that matter, any other language, falter in these so-called word-for-word translations. (Which are not even possible because Greek uses cases and the word order has to change in order for it to make sense in English!) my Greek teacher for 2 years was Bill Mounce, who is one of the top translators in the world, we used his material in seminary, and the second course I took online with Dr. Mounce.
The other important thing he says, is that Koine (common) Greek was a language in transition. The prepositions in particular, are very fluid. "Eis" is one that has different meanings, because it was an older word, being replaced by "en." The gloss, I would agree, is "into." But a glossary in a grammar book notes that eis is "into, in, among." Seriously, "into" is a word that is dying in English, so there is no need to pin it down as only meaning "into." Learn the Greek alphabet, then get Bauer, or BDAG, the best Greek lexicon. Then you can the full means of words. The alphabet isn't hard, and when you use it a bit, you will remember it.
Just because a translation translates a word a certain way, doesn't mean it is right. Some Bibles, like the ESV follow the "KJ tradition," meaning that the rely heavily upon an older translations. Looking it up in multiple modern translations can help to pin down the meaning. Sometimes a certain passage uses the preposition in the same way in every translation. Other times, things get more slippery. This might be a case where eis = into. I'll leave that to you to figure out. Just be careful about flatly translating. And if you are really interested in Greek, which I always was, study it, either in a class or online. You will be amazed at what you learn.
"Πέτρος δὲ [a]πρὸς αὐτούς· Μετανοήσατε, καὶ βαπτισθήτω ἕκαστος ὑμῶν ἐπὶ τῷ ὀνόματι Ἰησοῦ Χριστοῦ εἰς ἄφεσιν [c]τῶν ἁμαρτιῶν [d]ὑμῶν, καὶ λήμψεσθε τὴν δωρεὰν τοῦ ἁγίου πνεύματος·" Acts 2:38
For example:
"Peter said to them, “Repent, and each one of you be baptized[a] in the name of Jesus Christ for[c] the forgiveness of your sins, and you will receive the gift of the Holy Spirit." Acts 2:38 NET
The NET basically used "for" for, for eis. The NET Bible is renowned for its its 60,000 footnotes [c] is attached here. As you can see, it is much more complicated translating it, than you make it to be in your post.
"Acts 2:38 tn There is debate over the meaning of εἰς in the prepositional phrase εἰς ἄφεσιν τῶν ἁμαρτιῶν ὑμῶν (eis aphesin tōn hamartiōn humōn, “for/because of/with reference to the forgiveness of your sins”). Although a causal sense has been argued, it is difficult to maintain here. ExSyn 369-71 discusses at least four other ways of dealing with the passage: (1) The baptism referred to here is physical only, and εἰς has the meaning of “for” or “unto.” Such a view suggests that salvation is based on works—an idea that runs counter to the theology of Acts, namely: (a) repentance often precedes baptism (cf. Acts 3:19; 26:20), and (b) salvation is entirely a gift of God, not procured via water baptism (Acts 10:43 [cf. v. 47]; 13:38-39, 48; 15:11; 16:30-31; 20:21; 26:18); (2) The baptism referred to here is spiritual only. Although such a view fits well with the theology of Acts, it does not fit well with the obvious meaning of “baptism” in Acts—especially in this text (cf. 2:41); (3) The text should be repunctuated in light of the shift from second person plural to third person singular back to second person plural again. The idea then would be, “Repent for/with reference to your sins, and let each one of you be baptized…” Such a view is an acceptable way of handling εἰς, but its subtlety and awkwardness count against it; (4) Finally, it is possible that to a first-century Jewish audience (as well as to Peter), the idea of baptism might incorporate both the spiritual reality and the physical symbol. That Peter connects both closely in his thinking is clear from other passages such as Acts 10:47 and 11:15-16. If this interpretation is correct, then Acts 2:38 is saying very little about the specific theological relationship between the symbol and the reality, only that historically they were viewed together. One must look in other places for a theological analysis. For further discussion see R. N. Longenecker, “Acts,” EBC 9:283-85; B. Witherington, Acts, 154-55; F. F. Bruce, The Acts of the Apostles: The Greek Text with Introduction and Commentary, 129-30; BDAG 290 s.v. εἰς 4.f." NET
You can access all the footnotes in Biblegateway.com, for free! And if you are interested in Greek, don't rely in Concordances, but learn the alphabet and get a good quality lexicon, like Bauer, BDAG, which is what Biblical scholars use, and tax some classes!