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The name Blume (this spelling) is German for Flower.
I have heard of two possibilities for this family name. One, that it was someone's profession for which he became known, like Baker for a baker, or Miller for a miller. So, someone named Blume might have been a florist or similar. The other variant might be that a person's profession was painted on a shop sign back when not everybody was able to read. The symbol of the flower might then have shown who lived there or what their profession was. My mother told me these things, I have no other means of verifying this but would be interested in other information.
The variant of Blum might be Jewish, its later change into the English-language Bloom would be phonetic. Bloem might be Dutch (Bloemfontein for example, in South Africa - flower fountain. Blumental - flower valley/vale. Hope this helps! K Skillings, 2020