Don't pick anything in the top 100. Outside that you'll be fairly safe as long as don't pick something that's partially regionalised in nature like something like Seren and also live in that region.
The top ranking name was shared by 5,327 girls and 6,649 boys in England in Wales in 2014. But rank 100 was shared by 577 girls and 602 boys. You are around rank 250 for less than 200 babies with the same name and about rank 400 for less than 100 babies. So the number of babies goes done very quickly the further down the rankings you go.
The regional differences are massive. There are stats available for the top 100 for England, Wales, Scotland and NI. (There is also a break down by region for England and Wales for the top 10.
Here are a few comparisons - you need to allow for accents for some of these. Each of the numbers relates to rank in the top 100 of that particular region of the UK and doesn't include anything ranked lower than 100:
Carter is in favour in Wales (61) and NI (63), but in Scotland its cousin Carson is more popular (95). There are no 'Car' names in England though.
Allowing for regional accents there are a few different 'Cal' names knocking about. The most universal is Callum, which isthe only one found in England and Wales. However in Scotland you have a choice of spellings - Callum (21) and Calum (75) as well as Callan (80) or even Calvin (94). Over in Northern Ireland the option of Caolan is also on the cards.
Friendly Charlie makes it into the top 10 everywhere but the longer Charles only makes the top 100 in England (62).
Likewise, In NI the less formal Ben (38) is more common than Benjamin. Ben only makes the top 100 elsewhere in Scotland (51). Benjamin is considered best in England (28) and Wales (46).
However its just Sam in England and Wales but Sam and Samuel in NI and Scotland with Samuel being the more favoured.
In England it is most definitely Zachary (41) but in the rest of the country the shorter form of Zac is also an option in Wales and Scotland and Zach (65) is in fact the prefered choice over Zachary (98) in Northern Ireland
Ted might not make it into the top 100 anywhere but curiously its cousins Edward, Teddy, Theo and Theodore have very different fortunes. Edward only makes it in England and Wales. Teddy (66) and Theodore (56) make iit in England alone, but short snappy Theo is popular everywhere.
Finlay (15) is the prefered spelling in Scotland, with the shorter Finn at 63. However the spelling Finley (35) is prefered over Finlay (98) in England and is the only variant in the top 100 in Wales (23). In Northern Ireland on the shorter Finn (40) or the Irish Fionn (58) make the 100.
Harry is most popular everywhere but Scotland where Harris (12) edges it to 14th. Harrison also is in the top 100 everywhere but Harri makes an appearance in Wales (28) and the more formal Henry is in the top 100 everywhere but Scotland.
Logan is popular everywhere, but the similar sounding Lorcan also makes the top 100 in Northern Ireland.
Curiously Rowan makes a sole entry in Wales (74) whilst the similar sounding Ronan is the only entry in Northern Ireland (34).
Welsh Macsen (78) makes it into the top 100 in Wales as well as Max which is popular everywhere. Its is interesting for its similar sound to Mason which also makes the top 100 in all four regions. It is worth noting though, that the combined figures for England and Wales put Macsen way down at 583rd! Which really reflects how much regionalised names are favoured and are concentrated rather than being evenly spread throughout GB and NI.
The more fashionable Lucas come in over traditional Luke everywhere but Northern Ireland which also shuns Luca which makes it into the top 100 in England, Wales and Scotland.
Bobby over Robert in England and Northern Ireland, but Robert (50) over Robbie (77) in Scotland.