If you are thinking of applying for a copy of his death certificate from the GRO, you must order it exactly as it is in the index ie Admanson, not as you expect it to be spelt.
If you order it as Adamson, there is a good chance you will get a 'no trace' refund.
Alternatively, you can order it from the local register office (which will cost more) and explain it could be either spelling. The GRO doesn't have that facility.