The name "Lay the 'rump" might face challenges when being submitted for racehorse registration. The British Horseracing Authority (BHA) has strict guidelines for racehorse names, including the rule that names must not be offensive, vulgar, or suggestive(Horse & Hound)(British Horseracing).
Since "Lay the 'rump" could be interpreted as suggestive or in poor taste, it is likely to be rejected under these rules.