In English when you hold out something to someone, sometimes a vocal prompt like "here" or "there" is said to indicate that you are giving it to the person.
In Chinese (or at least in Singapore) we sometimes use something that sounds like "na" or even use the Chinese word "给(gěi)" as an expression while holding out something towards the recipient.
EDIT: Perhaps I should have been more specific about what I'm referring to. I'm not referring to giving "gifts", but just giving in general. Something like just passing a note to somebody or when someone looks in need of a tissue and you just hold it out to them.
(Question) What's the equivalent of this concept in Japanese? I ask because I think it feels quite awkward to either remain silent, or to form a complete sentence asking the person to receive it especially if you are familiar with the person.