It doesn't mean "strong". "Rocín" means "nag/work horse" (as opposed to war horse) and "antes" means "before" (here like "before and first of".

Cervantes himself explains the meaning:

EN
"Four days passed as he tried to imagine what name he would give him... and so, after many names that he formed, erased, and removed, added, undid, and made again in his memory and imagination, he finally decided to call him Rocinante, a name that seemed to him lofty, sonorous, and significant of what he had been when he was a 'nag, before' what he was now, which was before and first of all the nags in the world" (that is, "skin and bones"), but which Don Quixote still saw as "a better mount than the famous Babieca of the Cid and Bucephalus of Alexander the Great."

ES
«Cuatro días se le pasaron en imaginar que nombre le pondría... y así después de muchos nombres que formó borró y quitó, añadió, deshizo y tornó a hacer en su memoria e imaginación, al fin le vino a llamar Rocinante, nombre a su parecer alto, sonoro y significativo de lo que había sido cuando fue “rocín, antes” de lo que ahora era, que era antes y primero de todos los rocines del mundo» (es decir «piel y huesos»), pero al que Don Quijote aún seguía viendo como «mejor montura que los famosos Babieca del Cid y Bucéfalo de Alejandro Magno».