Titubea means "hesitates" or "falters." It's a less common word than simply saying "duda" (doubts), and it paints a more vivid picture of someone struggling to speak or make a decision.
In the song, José José uses titubea to describe his partner's hesitation when trying to say his name, suggesting her uncertainty and the emotional distance growing between them. This word beautifully captures the subtle signs of a relationship in trouble.
Have you ever felt like someone you love is slipping away, and you just can't figure out why? That's exactly what José José is singing about in "¿Y Quién Puede Ser?" He's noticed a big change in his partner. She's "pensativa" [pensive], "indiferente" [indifferent], and "distraída" [distracted]. He tries to look her in the eye, but she can't hold his gaze, almost as if she's afraid her eyes will give away a secret.
He's left wondering, "¿Y quién puede ser si es que no soy yo?" [And who could it be if it's not me?] He feels like he's been erased from her heart, and he can't comprehend who could possibly give her more love than he does. It's a heartbreaking feeling when someone you're with feels "inquieta" [restless] in your arms, always has an excuse to leave, and even stumbles over your name. You can really feel his pain and confusion as he asks again and again, "¿Quién me habrá borrado de su corazón?" [Who could have erased me from her heart?]