The existence of a Mitochondrial Eve isn't evidence of a bottleneck though. It's an artifact (or theorem) of statistics. If you have interbreeding lines, some lines die out, others continue. The species may continue even though the probability of any line dying out is one. At some point, all but one line must die out.
This doesn't mean that other women were not around at the same time as the "Eve" person. It only means that their mitochondria isn't still in the gene pool. Were we able to look at other gene, each one (or at least the ancient ones) would show ancestry to a single individual.
A similar artifact happens with family names.
The existence of a Mitochondrial Eve isn't evidence of a bottleneck though. It's an artifact (or theorem) of statistics I disagree. It certainly could be the result of a statistical anomaly, but that is far from being actual evidence of such. More likely, it is suggestive of a near extinction event for the human race.
If you have interbreeding lines, some lines die out, others continue.
The former case is not a requirement unless an actual bottleneck (i.e., a reduction in population) does occur.
A similar artifact happens with family names.
This is true; but that is an artifact of patriarchical naming (where half of the family name "dies out" in each mating, something that doesn't happen on the genetic side of the analogy).