Generally, someone who plays the trombone is known as a trombone player or trombonist. Professionally in orchestras and big bands, they are often referred to by position or number (i.e ‘Solo trombone,' ‘lead trombone’, or ‘trombone 1’).  The terminology does vary slightly based on the location and the type of the group they play in, but you’ll never be wrong if you just say trombone player!