Alexander Hollyer (1830-1900) was one of the Hollyers who emigrated to the USA from England, as did his two brothers James and Samuel. But research has shown that many bearers of the name came from elsewhere in Europe.
Things might not be what they seem. What I've descibed so far applies mainly to English Hollyers etc. If you hold either of the three names and live in the US, you must consider the possibility of a non-British origin. Many immigrants passing through Ellis Island were given new Anglicised names.
If you are a Hollyer, you might be connected to the Ukrainian family originally called Holiat (Goliath). They now carry the name Hollyer.
If you are a Holyer, you might descend from a Swedish family originally called Helgerson or a Swiss family originally called Holger. The 'Y' better matches the sound of the soft 'G'. The US 1880 census also shows some Holyers who came from Germany.
If you are a Hollier, especially if you live in the Southern States, the chances are that you descend from the French Hollier family from Nantes.