Alliteration (begin-rhyme) has pretty much lost out in favor to rhyme (end-rhyme). Though it has still been used sparingly, Edgar Allen Poe, "While I nodded, nearly napping..." or Dr. Seuss, "Horton Hears a Who!"
Here is a list of soccer teams that use alliterative names to very memorable effect:
Wolverhampton Wanderers (England)
Alemannia Aachen (Germany)
Figueirense Florianopolis (Brazil)
Seattle Sounders (USA)
Cracovia Krakow (Poland)
Kemi Kings (Finland)
The transition to rhyme and end of alliteration in the West took place between AD 750 to AD 1050, coinciding, more or less, with Christianization. I wrote a little more about it this week in my blog.