The discoverer gave the patriotic reason, that he had named the element for Gallia, the Latin name for France. The coincidence that gallus is Latin for a rooster, and that his own surname, Lecoq, is French for the rooster, was pointed out at once and has been repeated ever since. Whether the second reading was intended, quietly enjoyed, or only ever imagined by other people cannot be settled from the naming announcement, which offers the patriotic reason alone.
What would resolve this A statement of intent in Lecoq de Boisbaudran's own correspondence or working papers. Failing that, the question concerns a private intention and may simply not be answerable.
OpenHistory of chemistry, and French archival work on the Lecoq de Boisbaudran papers.Royal Society of Chemistry, Periodic Table: Gallium