Hello!

When talking about the sound of a drum, one can mention beat (usually drumbeat), pattern, rhythm, roll as in a roll of drums, or simply sound. By the way, to "beat the drum for" means to try enthusiastically to persuade people to support some idea.

I can't think of an 'official' onomatopoeia for a drum, like for cymals. Cymbals 'crash'. 

Drums could be a few things- a bass drum a like 'bom bom bom' and a snare drum is more like 'rat-a-tat'. Because there are so many parts to a drum kit perhaps that's why there isn't one. My advice is to create one, as I don't believe we have on in English!