Why is hexane called skellysolve-B
It's probably considerably notorious historical trade name. In many older publications, e.g. "Skellysolve B (petroleum ether)"[1,2] appears for solvent used.

It was a product or trade name of Skelly Oil Company[3]
 founded in 1919.

It's not a pure hexane, rather narrow-boiling hexane oil fraction.[3]

I could find analysis of similar product Skellysolve C, which is C7 heptane fraction:[3]


24.9% heptane
22.9%


2,3-dimethylpentane
2-methylhexane
3-methylhexane

19.3%


trans-1,2-dimethylcyclopentane
trans-1,3-dimethylcyclopentane

15.0% methylcyclohexane
5.5% cyclohexane
5.2% heavy nonaromatics
2.7% toluene
2.5% hexane
…


Other ones:[4]


  Skellysolve A is essentially n-pentane, b 28-30°/atm,
  Skellysolve B is essentially n-hexane, b 60-68°/atm,
  Skellysolve C is essentially n-heptane, b 90-100°/atm,
  Skellysolve D is mixed heptanes, b 75-115°/atm,
  Skellysolve E is mixed octanes, b 100-140°/atm,
  Skellysolve F is petroleum ether, b 30-60°/atm,
  Skellysolve G is petroleum ether, b 40-75°/atm,
  Skellysolve H is hexanes and heptanes, b 69-96°/atm,
  Skellysolve L is essentially octanes, b 95-127°/atm.


Unfortunately, Chemical Abstracts Service, mixes names for different substances, including this tradename: “n-hexane”, “hexane (all isomers)”, “Skellysolve B” under single CAS RN 110-54-3.[5]



References:


Newman, H.; Zilversmit, D. Quantitative Aspects of Cholesterol Flux in Rabbit Atheromatous Lesions. Journal of Biological Chemistry 1962, 237 (7), 2078–2084.
Holick, M. F.; DeLUCA, H. F. A New Chromatographic System for Vitamin D3, and Its Metabolites: Resolution of a New Vitamin D3, Metabolite. J. Lipid Res. 1971, 12 (4), 460–465.
Griswold, J.; Andres, D.; Berg, C. F. V.; Kasch, J. E. Pure Hydrocarbons from Petroleum - Separation of Straight-Run Fractions by Distex Process. Ind. Eng. Chem. 1946, 38 (1), 65–70.
Armarego, W. L. Purification of Laboratory Chemicals; Butterworth-Heinemann, 2017.
CommonChemistry.org – CAS Registry Number: 110-54-3