In August, the Office of National Statistics publish tables of names given to babies in the previous year in England and Wales. You can download an excel spreadsheet of the data from their web site. Scotland's General Register Office did the same for Scotland-born bairns back in March, available on their web site.
I always find it kind of interesting, but since I have a child born last year, I was especially interested to see the names. Our baby is called Alba. When I tell people this, they usually say "that's an ... interesting name" which I usually take to mean they think it is an unusual name - or perhaps not a real name at all. Maybe this is just my prejudice, as it was my reaction when my other half first suggested it. I didn't think it was a proper name that people actually had. She had seen it in the book The Time-Traveller's Wife and liked it from there. Fortunately, we had the 2012 baby name data to look at, and Alba came in at rank 483, with 91 Albas born in 2012. That's above Frances (89 of them), Veronica (77), Gemma (73), Bridget (52) and Caroline (28) but below Princess (97), Jorja (102), Lacey-Mae (107), Lillie-Mae (108), Gracie-Mae (123), Lilly-Mae (158), Lilly-May (179), Ellie-Mae (189), Lily-May (192), Ellie-May (207) and Lily-Mae (232). I was sufficiently convinced that Alba was a real name, and it grew on me.
Last year, there were 118 Albas born. Funnily enough, when we started going to baby activities and hanging out with other babies and their parents, we came across two other Albas in Guildford, making it the only name that multiple baby girls -- that we know -- have.
It's interesting seeing how once-common names have become uncommon, and that names I hadn't really heard of have become quite common. Take my own name -- Paul. In the year of my birth (1974) it was the most common boys name (in England and Wales at least, though I was born in Scotland), and had been moderately popular for some time before that. It didn't take too long to drop way down the ranking. The plot attached shows where Paul came in the boys name list for about a hundred year period. The graph of other once-common names looks pretty similar. In 2013, Paul was in position #285, off the scale on the graph I made a few years ago. Names more popular than Paul (in 2013) include Aryan, Zayn and Jace, which are all a bit unfamiliar to me, as well as some I'd have thought to be rather old-fashioned, like Sidney and Wilfred.
The ONS list for England and Wales give names only down to those with at least 3 occurrences "using S40 of the Freedom of Information Act in other to protect the confidentiality of individuals", so you can't see the really unusual and unique names, though names with three occurrences (amongst girls) include Weam, Wan, Tallulah-Blu, Shy, Ren, Pal, Meta, Lolly, Lava, Disney and Bellatrix. Boys' names occurring thrice include Ze, Tory, The, Rj, Pious, Pa, Or, King-David, Greatness and Berk.
Scotland's GRO shows no such qualms about showing names given to fewer than three babies, so if you follow the link above, and are so inclined, you can see all the one-off names given in Scotland.