I see. My own understanding of "suddenly" was more sudden...
I don't want to spam this forum with links to my own website, but I think my hitparade comparison feature is very handy here and right on-topic - it shows that between 2005 and 2013 the rise of
Liam is indeed noteworthy. However, there are quite a number of other names like
Eli and
Oliver that rose 100 or more places in the same time:
http://www.babynames.ch/Info/Hitparade/poUs2013m?compHitparade=poUs2005m
The important difference to
Liam is that those other names are nowhere near the top, at least not yet.