Is a bit string pseudorandom if it starts with predictable bits? Assume we have $k = n + m$ bits string $S$ where the first $n$ bits are predictable, and the last $m$ bits are pseudorandom (the HMAC of the first $n$ bits + IV). Can we say $S$ is a pseudorandom number? 

What can we call S exactly?
No, first of all, you've defined it to be a bit string. A bit string is not a number although you can of course interpret it as a specific number.

Furthermore, it is not pseudo-random if we assume that the number is between 0 and the maximum value for S, as it clearly is either in a range, or it ends with a lower end bits set to a specific value.

Now if we assume big endian then you can however consider $S$ pseudo random in the range $\Big[N \cdot 2^m, (N + 1) \cdot 2^m \Big)$ where $N$ is the big endian value of the first $n$ bits of $S$.

I don't know what we can call $S$, it's a constructed bit string. With the HMAC it could be some kind of token, but that's speculating on a specific use case for it.