"The Smashing Pumpkins" is name of band, and its meaning is pumpkins that are:
smashing
adj : very good; "he did a bully job"; "a neat sports car"; "had a great time at the party"; "you look simply smashing" [syn: bang-up, bully, corking, cracking, dandy, great, groovy, keen, neat, nifty, not bad(p), peachy, slap-up, swell]
(
http://dictionary.reference.com/search?q=smashing)
edit: I just looked up 'the' and the pronunciation is determined by whether it's followed by a vowel or consonant. I think I've been doing it randomly all these years..