You asked

I write to request the number of births registered in 2018 so far with the name 'Grayson'. In addition I would like to know the number of registrations with the alternative spelling ‘Greyson’.

We said

Thank you for your request.

Baby name statistics are compiled from first names recorded when live births are registered in England and Wales as part of civil registration, a legal requirement. The statistics are based only on live births that occurred in the calendar year, as there is no public register of stillbirths. The statistics are based on the exact spelling of the name given on the birth certificate.

Our latest baby name statistics are for England and Wales in 2017 (published on 21 September 2018) is available at:
https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/livebirths/bulletins/babynamesenglandandwales/2017

Table 6 in our published dataset provides all names registered in England and Wales in 2017 down to counts of 3; names with a count of 2 or less are redacted. Under s.39 of the Statistics and Registration Service Act 2007, personal information held by us (including that which identifies a body corporate), must not be disclosed. Because the release of this information is prohibited by law, s.44 of the Freedom of Information Act 2000 applies.

boys dataset: https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/livebirths/datasets/babynamesenglandandwalesbabynamesstatisticsboys

girls dataset: https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/livebirths/datasets/babynamesenglandandwalesbabynamesstatisticsgirls

In 2017, there were 588 baby boys named Grayson and 106 named Greyson. We are unable to provide figures for 2018 until the figures are published in summer/autumn 2019.