Histidine protonation In histidine structure , full protonation gives a structure with only the double bonded nitrogen having been protonated in the ring and not the single bonded nitrogen. Why is that?

Textbooks tend to report structures as relatively static, whereas advanced biochemistry texts explore structural tautomerism. In essence, the histidine imidazole sidecvhain may move around it's protons and electrons when pH is roughly equal to pKa. Thus, the sidechain exists as two tautomers where the two nitrogens sort of "share" the double-bond character and the proton, like so:

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And it's even more accurate to depict that the double-bond character is like so:

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