Jesus came for the lost yet He did not say all people are lost.
He is not recorded as having said the actual words, "All people are lost," but He often said that only those who believe in Him would be saved to eternal life. For instance:
“"And as Moses lifted up the serpent in the wilderness, even so must the Son of Man be lifted up, "that whoever believes in Him should not perish but have eternal life. "For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life.” (Joh 3:14-16 NKJV)
He never said, "By obeying God's commandments you will be saved."
He certainly did not offer salvation to John the Baptist even if John the Baptist did not know Christ's birthname and died never knowing His birthname.
We don't read in the bible an account of Jesus "offering salvation" to John, but that doesn't mean that He didn't do so. John would be included in "whoever believes in Him." John did believe in Jesus. He said:
“Behold! The Lamb of God who takes away the sin of the world!” (Joh 1:29 NKJV)
Where do you get the idea that John didn't know the birthname of Jesus? Granted, he doesn't refer to Jesus by that name, but seeing as John was the son of Elizabeth, a relative of Mary, he would have known it.
The word used for "name" in Greek (original translations of the New Testament teachings) doesn't only mean birth name but can also be "cause".
The vast majority of Christians assume that believing in the "name" of Jesus meant believing in His birthname which would mean John the Baptist died unsaved which is definitely NOT the case.
Not so. The word for "name" can mean "cause", but it means other things as well. My bible dictionary says:
"1) name: univ. of proper names
2) the name is used for everything which the name covers, everything the thought or feeling of which is aroused in the mind by mentioning, hearing, remembering, the name, i.e. for one’s rank, authority, interests, pleasure, command, excellences, deeds etc.
3) persons reckoned up by name
4) the cause or reason named: on this account, because he suffers as a Christian, for this reason"
I cannot think of anybody who believes that the label "Jesus" actually saves. I believe "name" as far as Jesus is concerned means His whole Person and character, as described in 2) above. We are told why He was to be given the name "Jesus":
“"And she will bring forth a Son, and you shall call His name JESUS, for He will save His people from their sins."” (Mt 1:21 NKJV
John definitely worked for the Lord's "cause" and therefore believed in His "cause" (in context but translated in English as "name")
He did, but He believed that Jesus is the Saviour. He believed Jesus was far more important than him.
There are many good and selfless people around world working for the Lord's "cause" without knowing His birthname and many aren't even Christians.
How can anybody work for God's cause who doesn't believe in His Son? Jesus spoke about His heavenly Father's will, His "cause", like this:
“"And this is the will of Him who sent Me, that everyone who sees the Son and believes in Him may have everlasting life; and I will raise him up at the last day."” (Joh 6:40 NKJV)
The Lord's cause can be summed up to the first two commandments. People who never heard about Christianity nor the Bible can end up doing the Lord's cause by simply loving others as themselves especially people who are poor (Matthew 25:40).
But loving others, though important, is only one of the two commandments you mention. The first, Jesus said, is:
“‘And you shall love the LORD your God with all your heart, with all your soul, with all your mind, and with all your strength.’ This [is] the first commandment.” (Mr 12:30 NKJV)
It's entirely possible for people in isolated communities to be saved in spite of lazy, greedy, pleasure-seeking Christians not doing enough to help spread the Gospel to the world. It would be a huge injustice that God would send good and selfless people to hell because His selfish, greedy, worldly, pleasure-loving followers can't be bothered to break a leg from their comfortable lives.
"name" in Greek:
ὄνομα - onoma
NAS Exhaustive Concordance
Word Origin
a prim. word
Definition
a name, authority, cause