I am doing Customer Support and I need to tell my user that their phone is from "a less well known" brand (e.g. from Xiaomi instead of Apple, Samsung). Which words to use in this courtesy context?
You can tell the person that their phone is "off-brand." It means the brand isn't a well-known.
The OP could inform customers that they are using a low-end brand or a low-end model
low-end (The Free Dictionary)
1. Cheapest in a line of merchandise
2. Informal Of, relating to, or intended for low-income consumers; downscale
Otherwise, the OP could simply say that the customer's phone is not a top brand. I believe that phrasing is the least equivocal, less offensive (or derogative) and the easiest to understand.
A: I have a problem with my cell phone, it's a blah, blah
B: OK, it's not a top brand, but we can still help you.
B: OK, it's a low-end model (or brand), but we can still help you.
I asked my baker for a croissant. "Butter or ordinary", she said with a depreciative tone on the last word. I bought the butter one... I propose ordinary or generic. Generic brands seem to be used in supermarkets.
But off-brand by @Benjamin Harman is excellent.
EDIT: as the answer above is checked as the best (deserved), let me add options for the sake of completeness: for smartphones, cheap and low-cost are quite related to the fame of a brand. Fuels exist in regular and premium. Standard was my last option.
Low-end or off-brand connotes something that is cheap and is of low quality. Generic means that the item does not carry a brand at all; i.e a box of tissues that is marked "Tissues". Ordinary just means the same as any other; i.e. an ordinary can opener just opens cans, while a deluxe model may have a corkscrew or a knife sharpener included.
You were on the right track to begin with. It's fine to say a lesser-known brand. (Note: not a "less well known brand."