To "declare" means to say something formally, publicly and with emphasis; you might say what you think, but you only declare things you're sure of. So just as saying relates to sharing truth at various levels, "declaring" relates to sharing fundamental, unquestioned principles, often those that reveal the Lord and the salvation that lies in His embrace.

In Amos 4:12-13, 'to declare' signifies to flow in.

(Ссылки: Apocalypse Revealed 478; Arcana Coelestia 7550, 8762)

7550. 'And in order that My name may be declared in the whole earth' means that thus the Lord may be acknowledged, where the Church exists, as the only God. This is clear from the meaning of 'name' as everything in its entirety by which the Lord is worshipped, dealt with in 2724, 3006, 6674, and since the most essential aspect of worship is the acknowledgement that the Lord is the only God, that His Human is Divine, and that from His Human emanates everything of faith and love, 'Jehovah's name being declared' means that the Lord should be acknowledged as the only God (for the Lord's Divine Human is 'the name of Jehovah', see 2628, 6887); and from the meaning of 'the earth' as the Church, dealt with just above in 7547. When it says here and in very many other places that Jehovah or the Lord desires His virtue or power to be seen, and His name to be declared, and elsewhere that He desires people to worship and adore Him in humility, it seems as though He desires to display His glory and loves to be adored for His own sake. But the truth of the matter is altogether different. It is not for His own sake but for that of the human race; He is moved not by self-glory but by love. For He wishes to be joined to the human race, and to impart eternal life and happiness to it. But this cannot be accomplished unless a person worships Him in humility; and such humble worship does not exist unless the person acknowledges and believes that he himself is dust and ashes, that is, nothing but evil, that Jehovah or the Lord is the Greatest and Most Holy One, and that of himself he does not dare to approach Him. When a person worships Him in such humility the Lord can enter in with the life of His love, bringing him heaven and eternal happiness. This is the reason why Jehovah or the Lord extols His power and glory to so great an extent in the Word.