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‘Here,’ said Elrond, turning to Gandalf, ‘is Boromir, a man from the South’.

Since Gandalf had visited Minas Tirith many times and was well-known to both Denethor and Faramir how was it that he didn't already know Boromir?

They certainly could have met

Boromir was born in 2978, Faramir in 2983 and Denethor became Steward of Gondor in 2984.

2978 Birth of Boromir son of Denethor II.

...

2983 Faramir son of Denethor born.

...

2984 Death of Ecthelion II. Denethor II becomes Steward of Gondor.

_{The Lord of the Rings Appendix B, Section 2: The Third Age
Page 1090 (Houghton Mifflin Harcourt; Single Volume 50th Anniversary Edition)}

Faramir tells Frodo that he met Gandalf when he was a child and that Gandalf had visited Minas Tirith.

I first saw him when I was a child, and he has been twice or thrice since then.’

‘The Grey Pilgrim?’ said Frodo. ‘Had he a name?’

‘Mithrandir we called him in elf-fashion,’ said Faramir, ‘and he was content. Many are my names in many countries, he said. Mithrandir among the Elves, Tharkûn to the Dwarves; Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not.’

_{The Lord of the Rings Book Four, Chapter 5: The Window on the West
Page 670 (Houghton Mifflin Harcourt; Single Volume 50th Anniversary Edition)}

We know that Gandalf's last visit to Minas Tirith before war breaks out is in 3017 when he finds Isildur's description of the Ring.

3017 Gollum is released from Mordor. He is taken by Aragorn in the Dead Marshes, and brought to Thranduil in Mirkwood. Gandalf visits Minas Tirith and reads the scroll of Isildur.

_{The Lord of the Rings Appendix B, Section 2: The Third Age}

There is no mention of Boromir ever meeting Gandalf during these visits and it is always possible that Boromir was not in the city at these times.

There is nothing in The Council of Elrond to suggest that Gandalf and Boromir recognise each other. While they would certainly know the other's name, perhaps we should assume they had never met.

Gandalf likely at least knows of him, as the heir apparent to the Stewardship of Gondor. We see much later in RotK that Gandalf knows Denethor, so it stands to reason that he would also at least recognize his son by name. But all we really get here is that Elrond doesn't know him:

‘Here,’ said Elrond, turning to Gandalf, ‘is Boromir, a man from the South. He arrived in the grey morning, and seeks for counsel. I have bidden him to be present, for here his questions will be answered.’

Apparently all that Boromir has said of himself by this point is that he came from the South, so there's no reason for Elrond to assume that anyone else present should know him. Boromir doesn't identify himself as Denethor's son, or even being from Gondor, until later in the conversation, but we don't then see any reaction from Gandalf or anyone else.