In Jewish (or Semitic) culture, someone's 'name' was their authority, reputation or their status. For lack of a better description, they were their 'name'. It wasn't just the word you use when you address them—and was seen as a distinct thereto, insofar as it could function without mention of a specific 'word'.
As such, when this angel 'had' יהוה (YHVH), God's name (Isa 42:8), He was, for all intents and purposes, YHVH Himself—more than a mere representative or 'common angel.'1
Although the identity of the angel is unknown, we have two great candidates:
- Michael (Dn 12:13,21)
- מלאך יהוה malak YHVH—the Angel of YHVH (Ex 3:2)
Of these two, the latter is the most likely candidate by far, for we see in Scripture elsewhere his perogatives are those of God: that is, wherever we read of the Angel of the LORD in Scripture, he is [simply interchangable with YHVH/God Himself most of the time.2
The example you give is a key one; elsewhere it is a key description and perogative of the Jealous God Himself (Ex 34:14), YHVH (notice that this characteristic distinguishes Him as God, since we are to recognize by it that He is a just, or jealous, God):
Joshua 24:19 (NASB)
Then Joshua said to the people, "You will not be able to serve the LORD, for He is a holy God. He is a jealous God; He will not forgive your transgression or your sins.3
That is, 'forget about thinking yourself able to do x.' Making, as Abu Munir noted is a warning (that is, 'allowed to do x') in the context of Exodus 23:20-21.
As for the passage in 1 Corinthians 10:9, it is a reference to the comparison made between trust in and fidelity to Jesus for salvation, and the sign unto which they were to look (a pole with a serpent upon it) who wished to be saved from the judgement of God (in the form of venomous snakes):
Numbers 21:5-7 (NASB)
The people spoke against God and Moses, "Why have you brought us up out of Egypt to die in the wilderness? For there is no food and no water, and we loathe this miserable food." The LORD sent fiery serpents among the people and they bit the people, so that many people of Israel died. So the people came to Moses and said, "We have sinned, because we have spoken against the LORD and you; intercede with the LORD, that He may remove the serpents from us." And Moses interceded for the people. Then the LORD said to Moses, "Make a fiery serpent, and set it up [for a sign]; and it shall come about, that everyone who is bitten, when he looks at it, he will live." And Moses made a bronze serpent and set it up [for a sign]; and it came about, that if a serpent bit any man, when he looked to the bronze serpent, he lived.
To which Jesus makes reference in John 3, comparing Himself as the hope of their eternal salvation to the serpent upon the pole ('lifted up' meaning to be crucified on a cross) which was for them their hope of temporal salvation:4
John 3:14-15 (NASB)
As Moses lifted up the serpent in the wilderness, even so must the Son of Man be lifted up; that whosoever believeth in him, may not perish; but may have life everlasting.
However, it's not necessary to take St. Paul to be saying that those who tempted God in the desert were tempting Christ, since the text itself only describes a certain punishment (a judgment of some kind) for a certain fault (tempting the Lord): that is, the example is analogical, not specific.
The Greek of 1 Corinthians 10:9 can be translated as follows:
Let us not tempt Christ [or, the Lord] 5 as they tempted [the Lord? Christ?—doesn't matter; doesn't specify] who perished by [the venomous] serpents.
"As Moses..so the Son of Man.." Jesus could be being compared to Moses in the role of chief intercessor, since both "the LORD" and "Moses" were 'tempted' (Num 21:5a).6
The Unforgivable Sin
The so-called unforgivable sin is not unforgivable on the part of God, neither is He unwilling or unable to forgive such sins (nor again is Christ and the Holy Spirit of a different dignity or whatever else—note that 'Son of Man' is a title of "the man Christ Jesus" 1 Tim 2:5b): it is precisely on the part of the sinner, who "offers an affront to the Spirit of grace" Heb 10:28-30 who cannot be forgiven for that very reason—he has pushed aside forgiveness itself; he has apostatized. Because it is the Spirit who administers forgiveness: Jn 20:22-23; Mk 3:30. One will note well that Christ elsewhere states that apostasy or denial of the faith is unforgivable, for example, and that Luke puts this right in the context of the unforgivable sin (Lk 12:9).
If God's 'jealously' or His justice are connected with 'not forgiving' transgressions against him (whereas an angel might do so), which I beliebe is borne out by the texts linking them, then His warning might simply be to identify the angel as that Angel of the LORD who, as said before, is virtually synyonmous and identical with YHVH Himself—as מלאך יהוה. By ascribing to him His own perogatives with which they ought to be familiar.
1 Hebrews, for example, which describes the Son as the intrinsic expression of the eternal God (1:3), gives to Jesus the Name proper to God alone "the name above every name"—LXX Kyrios which however answers to the Tetragrammaton in the Masoretic (Heb 1:4,10; cf. Phil 2:10; Jer 23:6).
2 cf. Zech 3:4; Isa 43:25; Lk 5:21; Mk 2:7 | See: Don Stewart, Who Is the Angel of the Lord in the Old Testament?.
3 cf. Ex 23:20-21; Deut 29:20
4 cf. Jn 12:34
5 [See NA27 variants] There is a variant in 1 Cor 10:9—..should not test τὸν κύριον |or| Χριστόν (the Lord |or| Christ). For the purposes of the answer, either could be referring to the preincarnate Son, as each are proper titles thereof.
6 Num 21:5a; cf. 1 Tim 2:5; Rom 8:34; Heb 7:25; 10:29