Octave-spanning, self-referenced frequency combs are applied in diverse fields ranging from precision metrology to astrophysical spectrometer calibration. In the past decade, Kerr frequency comb generators have emerged as alternative scheme offering chip-scale integration, high repetition rate and bandwidths that are only limited by group velocity dispersion. The recent observation of Kerr frequency combs operating in the dissipative Kerr soliton (DKS) regime, along with dispersive wave formation, has provided the means for fully coherent, broadband Kerr frequency comb generation with engineered spectral envelope. Here, by carefully optimizing the photonic Damascene fabrication process, and dispersion engineering of $\mathrm{Si_{3}N_{4}}$ microresonators with $1\,\mathrm{THz}$ free spectral range, we achieve bandwidths exceeding one octave at low powers ($\mathcal{O}(100\,\mathrm{mW})$) for pump lasers residing in the telecom C-band ($1.55\,\mathrm{\mu m}$), as well as for the first time in the O-band ($1.3\,\mathrm{\mu m}$). Equally important, we find that for THz repetition rate comb states, conventional criteria applied to identify DKS comb states fail. Investigating the coherence of generated, octave-spanning Kerr comb states we unambiguously identify DKS states using a response measurement. This allows to demonstrate octave-spanning DKS comb states at both pump laser wavelengths of $1.3\mathrm{\,\mu m}$ and $1.55\,\mathrm{\mu m}$ including the broadest DKS state generated to date, spanning more than $200\,\mathrm{THz}$ of optical bandwidth. Octave spanning DKS frequency combs can form essential building blocks for metrology or spectroscopy, and their operation at $1.3\mathrm{\,\mu m}$ enables applications in life sciences such as Kerr comb based optical coherence tomography or dual comb coherent antistokes Raman scattering.