I bought a small evergreen tree at least ten years ago. It has flowers
on the underside of the branches in May/June and is very slow growing
more out than upwards. However, unfortunately, it was being obscured by
a cherry tree, so I decided to replant it, but alas it looks to be
dying, but I cannot remember the name of it. Can anyone identify it
please.

This appears to be a conifer which would not have flowers.
Can you provide a better picture?
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Monterey, California USA
USDA Zone 9
Sunset Zone 17