You can pronounce 11001 in binary (so 25 in decimal) as "eleven thousand and one in binary".
Let me be clear: I represent a minority view, and am aware of this.
In his answer, dxiv says that "the names of numbers are used to denote the numbers themselves [(quantity they represent)], not some particular representation of them" (italic is my addition). That is an opinion one can have. For me, "the names of numbers are used to denote a particular representation of quantity, not the quantity that they represent. That is also an opinion.
In a comment, Octopus said that it is "incredibly misleading" to read binary 11 as "eleven". Octopus probably says this because he is of the opinion that "eleven" is used for 1+1+1+1+1+1+1+1+1+1+1, while binary 11 stands for 1+1+1. But it is only misleading because we should mention the base system in both cases: I read "binary 11" as "binary eleven", just as I read "11" as "eleven".
I would say that it is misleading to say that "eleven" always stands for 1+1+1+1+1+1+1+1+1+1+1. If we write numbers in digits, we should be clear about which base is used. I believe that we should also do this when we "say" numbers.
So for me, "1000" is always read as "thousand". In base 2, base 4, base 10, base 64, whatever. The quantity that "thousand" represents, depends on the base, just as the quantity that "1000" represents. I don't see anything misleading about that.
Talking about the binary 1011, I would be confused if somebody reads this as "eleven". If we have established that we are working in a binary system, it is confusing to use the decimal system without warning. It is perfectly acceptable, and not ambiguous, to call this "decimal eleven" or "eleven in decimal". Or "binary one thousand and eleven". Or, because we have already established that we are talking binary, "one thousand and eleven".
What happens in practice: binary numbers get too large easily, so we spell the digits: "one oh one one".
Edited to add: I find it difficult to express why I would read "101" as "hundred and one" regardless of the base, because it is so obvious and natural to me.
I distinguish three different concepts related to a number:
- A. The quantity ($1+1+1$)
- B. The written notation ("3")
- C. How to say a number ("three")
Compare it to the three concepts related to a word (example: cat):
- A. The underlying concept (the animal that says "meow")
- B. The written notation ("cat")
- C. How to say this (/'kæt/)
If we go to a different base, for me it is like going to a different language. If I switch from English to German, the written notation changes (to "Katze"). If I read this word out loud, I don't say /'kæt/, but I (try to) say it the way that Germans do.
For me, reading $101_2$ as "five" is just as silly as reading "Katze" as /'kæt/. If you do that, you are mixing up languages in a (for me) very confusing way.