Although common, it is hard to give a specific name without seeing the flowers coming soon. It is a Trichocereus (Echinopsis if you want to be technically correct). There are many similar looking species/hybrids/cultivars. Please post again when the flowers open.

Nicely grown plant you have there...

Brad

I will repost when it blooms. However, the flower is very remniscent of a white chrysanthemum with thin, pointed petals about 3" across.
hortster

Well, after 22 or 23 days it finally bloomed last night. They have already started to close - when the blooms are full they are more flat, side to side. Here are the photos - I would love to learn the species name. Thanks!
hortster
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Horster,

I don't know the species, but Brad's got the right genus name - you can tell it's an Echnopsis (a South American genus, btw) from the longnecking of the flower. Bats or moths are its pollinator (hence it opening at night and being white-coloured).

And it's probably not a hybrid (since it opens at night and it flowers white). But there are many Echinopsis so sorry I don't know the exact species.

Common name may be Easter lilly cactus or sea urchin. Have fun researching.

I agree that it is a lovely plant!

Noto makes a good point - the hybrids are made with the intention of bright flower colours, and white isn't (usually) in the bright-colour spectrum.

I misspelled the genus name - it's 'Echinopsis'.

Thanks much to all for pointing me in the right direction. After going through a number of species with similar appearance, I will settle for just 'Echinopsis'.
hortster