Near as I can tell
"But one in a certain place testified, saying, What is man, that Thou art mindful of him? or the son of man, that Thou visitest him?" (Hebrews 2:6)
The writer of Hebrews is speaking of David though they don't identify him by name (see Psalm 8:4-5). The writer of Hebrews doesn't identify themselves, either. And while it's comforting to know who penned the Word of God--the very words that we have been given to reorient our thinking in this world--it's not necessary, I guess. While I'm not a professional theologian or Bible scholar, the tenor of the epistle seems to flow in line with the other things Paul wrote. But since it doesn't explicitly say, I suppose it's not my place to wrangle and wrestle out some answer where none is provided.
But look at what they're quoting. That's where it's at. They (Hey, it could've been a woman who wrote it. I've heard that argument.) are reiterating the astonishment of David that God would take notice of us. That He would essentially stoop to our level to see how things were going, maybe die for us if need be. And I don't mean to be flippant, need was. "Though the Lord be High, yet hath He respect unto the lowly..." (Psalm 138:6a)
The son of man that thou visitest him...
With that word "visitest comes the idea that God is inspecting, selecting, looking out for, watching. The same idea is expressed in the story of the Prodigal Son. Where Jesus speaks of the Father waiting and watching for His child to return."And he arose, and came to his Father. But when he was yet a great way off, his Father saw him, and had compassion, and ran, and fell on his neck, and kissed him." (Luke 15:22) We're not anonymous to God. It's when we dwell on the goodness of God to seek us out, one by one, and establish a one-on-one relationship with us that we see the enormity of the Call. Let alone the fact that He made us in the first place.
"For Jacob my servant's sake, and Israel mine elect, I have even called thee by thy name: I have surnamed thee, though thou hast not known me." (Isaiah 45:4)
This is God speaking to King Cyrus, letting him know that even though he subscribed to a different pantheon, and didn't know the God of the Hebrews at all, that wasn't going to stop God from calling him out by name, using him for His purposes, and naming him (an additional name is the connotation in the Hebrew). The name Cyrus essentially means "sun king". "King Cyrus" is almost redundant--or resplendent, depending on how you look at it. Point is, God is working through him to secure a stable future for His kids. He says the same thing to His children in Isaiah 43:1, "I have called thee by thy name; thou art mine."
As far as I can tell
"He telleth the number of the stars; He calleth them all by their names." (Psalm 147:4)
God is an individual who has taken pains to re-reveal Himself to the world. Not just through His Son, but through the Body of Christ.
"But Christ being come an high priest of good things to come, by a greater and more perfect tabernacle, not made with hands, that is to say, not of this building." (Hebrews 9:11)
Here, the writer of Hebrews is referring to Jesus establishing "the temple of His body" (John 2:21). As the letter to the Hebrews is essentially a guidebook on transferring from one Covenant to another, from an outward dwelling of God, to an indwelling by the Spirit, it's fitting that the author would refer to Christ forming a place "not made with hands", i.e. something that God Himself has made. And while the writer of Hebrews says God put us "over the works of Thy hands", the building "not made with hands" is talking about our spirit. The essence of who we are minus our body. It's who God sees first when He looks at us. It's who He uses, anonymous or not, to get His business done in this world. How many times do you interact with people who don't know your name? Who don't know you from Adam? I would say a lot of our human-to-human interaction takes place without learning one's name. And as we represent God, essentially symbolizing Him to the world at large, it's Him who we're meant to leave an impression of. Anonymous or not.
John says "No man hath seen God at any time" (1:18). Granted, there are places in the Bible where God speaks to people face-to-face (Moses, Jacob, Job, etc.) and that's true. But I believe what John's referring to is our being able to precisely define His features as we would any human being. That's something that Jesus had to stand in for.
"Ye worship ye know not what: we know what we worship: for salvation is of the Jews. But the hour cometh, and now is, when the true worshippers shall worship the Father in spirit and in truth: for the Father seeketh such to worship Him. God is a Spirit: and they that worship HIm must worship Him in Spirit and in truth." (John 4:24)
"For the eyes of the Lord run to and fro throughout the whole earth, to shew Himself strong in the behalf of them whose heart is perfect toward Him." (2 Chronicles 16:9)
God calls us by name. A name that He thought up and that fits us perfectly. It's our place, now, to respond.