In the book The Odyssey, why must Odysseus disguise himself as a beggar because he still looks the same for Penelope to recognize him?
Odysseus must describe himself as a beggar because he wants the element of surprise on his side when he confronts the suitors. Remember that Odysseus has already been told that the suitors must die. His disguise is not something that he has just thrown together himself, Athena, the goddess of wisdom, is helping Odysseus. She is the one who told him that it would be wisest to go to Ithaca wearing a disguise. Athena is actually the one who cloaks Odysseus in his beggar disguise. She has not simply dressed him in rags, but she has made him look old and ragged. His face is covered in a graying beard and he has the appearance of an old man. In fact, in Book 16 Athena can hardly contain herself when father and son are so close to one another in Eumaeus' home that she beckons Odysseus outside where she proceeds to lift his disguise, changing him from young to old. When Telemachus lays eyes on the once old and tired beggar he is certain that it is a god because the transformation is so great. Athena replaces his disguise and Odysseus goes into his palace as the beggar and Penelope doesn't even recognize him, allowing him to hold fast to his element of surprise.
There are good practical reasons for Odysseus's disguise. Taking on the appearance of a beggar enables him to test the loyalty of a number of characters in the story. When Odysseus, disguised as a beggar, arrives at the swine-herd Eumaeus's hut, he spins an elaborate tale, pretending to be someone else. He also tells Eumaeus that Odysseus is on his way home to Ithaca. But Eumaeus doesn't want to get his hopes up, and in his weariness it's clear that his love and regard for his king is undiminished after all these years.
Odysseus has been away from home for twenty years. He's King of Ithaca and needs to have some degree of assurance that his kingdom is stable and secure. It's important, then, for him to know which people he can rely on. He knows he can't rely on Penelope's suitors, of course; they're his enemies. They've disrespected himself, his wife and his throne. But he does need to get some idea of what kind of men he's dealing with before he puts his battle plan into existence. And the disguise of a lowly beggar enables him to do this, allowing him to get up nice and close to the suitors so he can size them up before the big conflict ahead.