No name, no signature, no card. He hasn't done well starting out balance wise, but very clearly the light, fine grain, reclaimed wood that bares writing has been worked by hand and by heat. Maybe if Shoto's writing, designed in darker, purposefully charred areas on the sign weren't so distinct, it would be less obvious. Maybe if he hadn't used a very warm finger to heat carve "Dynamight" in English on what looks to be something that could be hung on a door, it would be less obvious. Given that it has a reclaimed bit of rope to hang it and a small hole in the two upper sides, that's probably what it's for.

Alas, it is obvious, but it is the gift that Shoto has at the moment, done in his spare time, done away from eyes that would otherwise have spoiled the surprise by seeing the work he was doing.

If it were any other day but Bakugo's birthday, then maybe it wouldn't have been a birthday gift. However, there it is, settled where Bakugo will certainly find it on the day of his birth. Shoto knows making a big deal about his birthday right now may not be what the hero wants, but the day is still precious and important to him because so is his friend.