When you want to be gentle?

[Borislav]

Is there any not so popular word when people say giving something to someone ?
I think except "for you" and "here" there is no ?

[Milanya]

I would like you to accept this little souvenir as a sign of my profound respect for you.
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con·text - The part of a text or statement that surrounds a particular word or passage and determines its meaning.

[Borislav]

ok .. if you are not joking )
it sound very formal

[Milanya]

It sounds formal because it is formal. You have given as little context as possible therefore you cannot count on a concrete answer. It depends on what you are giving, whom you are giving it to, for what reason, etc.
If it is a present for an occasion you might just say "Happy Birthday!" or "Merry Christmas!" and then hand a present.
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con·text - The part of a text or statement that surrounds a particular word or passage and determines its meaning.