There is a passage in the Iliad in which Diomedes and Glaucon recount their genealogies. This is about 6.140 in Fagel's translation.

So the plot here is Diomedes is under instructions from Athena to fight the Trojans but to stay away from the gods fighting on the Trojan side. It's rather a confused passage because Athena promised Diomedes would be able to know gods on sight, but Diomedes still has to ask:

Who are you, my fine friend? -- Another born to die?.... But if you are an immortal come from the blue, I'm not the man to fight the gods of heaven.

So they exchange genealogies and discover they have a guest-friend relationship through their grandfathers. Diomedes says

Come, let us keep clear of each other's spears... plenty of Trojans there for me to kill... and plenty of Argives too -- kill them if you can. But let's trade armor. The men must know our claim: we are sworn friends from our fathers' days till now!"

So they do this jersey swapping thing. I think this is one of the only places an authorial voice comes out in Homer - the poet is completely confused by this and says Glaucon must be confused because his armor was worth ten times' Diomedes.

In Greek epic identifying yourself is always a big deal - think of Odysseus telling the Cyclops (after the "my name is Noman" joke "I am Odysseus son of Laertes King of Ithica." But this particular bit about gift giving is associated in Homer at least with guest-friendships. Odysseus' bow was such a gift.

To some extent the tradition continued with proxenoi. Thucydides mentions that Alcibiades had a proxenos relationship with a Spartan Archon.

EDIT: Filling in holes I noticed. The point is the kind of relationship the OP is asking about existed in the Greek epic tradition, and something like it existed in historical times. A proxenos was a private citizen who had a relationship, often inherited, with a foreign city and acted as their point of contact in the proxenos' city. Here's a bit of the speech Thucydides makes Alcibiades give to the Spartans (6.89 - the Landmark translation):

The connection with you as your proxeni which the ancestors of our family by reason of some discontent renounced, I personally tried to renew by by my good offices toward you, in particular upon the occasion of the disaster at Pylos. But although I maintained this friendly attitude, you yet chose to negotiate the peace with the Athenians through my enemies, and thus strengthen them and discredit me.

The context for this is Alcibiades trying to defect to the Spartans. He's trying to convince them to take him in. Given Thucydides' problem with speeches it's unlikely that this represents even a gist of what Alcibiades said, but it does represent the gist of what Thucydides thought was necessary, or at least what would be believed, and illustrates how the hereditary relationship of proxenoi might have worked in war time. Alcibiades stresses the exchange of favors, which he claims the Spartans failed to uphold on their end and in fact worked against him in spite of his efforts. This (at least in my reading) gives him leverage both for asking sanctuary from Sparta, and for his plans of continuing the war against Athens.