Hi Gerry More,
The business name you would declare when registering for a Self Assessment Tax return, is used mainly to identify a different trade, where you have more than one self- employment trade and is for Self Assessment purposes only.
It is not registered in any way and as the letter advising you of your 10 digit UTR number is standardised, it will not show your business name, as the UTR number covers all sources of world-wide income, not just self- employment.
Expenditure incurred on advertising to establish a market share for a new product or brand may be capital.
An asset of this type is normally developed from scratch in-house although it may occasionally be built up from the acquisition of a struggling brand name or the rights in an invention.
BIM35640 - Capital/revenue divide: intangible assets: expenditure developing a brand name