This is one of those questions that will have a different answer depending on who you ask. The ultimate answer is the one that is most commonly used in paganism: whatever works for you. But some will say yes, an altar is of course necessary, while others say no.
What is an altar in the first place? Merriam-Webster defines “altar” as: “a usually raised structure or place on which sacrifices are offered or incense is burned in worship —often used figuratively to describe a thing given great or undue precedence or value especially at the cost of something else.” This is pretty much accurate in describing how pagans use an altar. It is a place that we use to conduct ritual, whether personal or in groups, and to offer prayer or sacrifice. (It’s also a nice place to burn candles or incense safely as it’s usually open and free from encumbrance, unless your altar is in your closet and could catch your clothes on fire.)
I didn’t have an altar for the longest time. Partly because I didn’t have a place for one, but also because I was still exploring and I felt it would only complicate my growth to add too much at once. But most of the pagans I know have an altar. I know one who keeps it in her closet on top of her dresser. Another uses the top of a bookcase. I like a wider surface, so lacking a table I like I use instead a three-drawer plastic tower that keeps my things safe from my cat and a three-shelf wooden tower right next to it. On mine I keep a statue of the deity I tend to look to the most, Athena, and I keep representatives of the elements: a feather for air, stones for earth, seashells for water, and a candle for fire.
There are different kinds of layouts for altars, which you can find all over the internet. On mine I lay my elements out according to which cardinal direction they correspond to and their season (example–earth is placed in the north and winter while fire is placed in the south and summer). Some will say that it is absolutely necessary to include chalices on the altar, and a wand, and other things. Well, I don’t have chalices just yet, and I haven’t noticed any deficiency in my altar.
What matters most in creating an altar is that you not only feel a connection with what you place there, but it is a clear space that you use only for the altar. Keep it clean and keep it clear of any other things that could be distracting or could influence the energy of the altar. Also construct it safely–if you burn candles or incense there, make sure there are no fire hazards.
Me, I don’t allow anyone else to touch my altar things, and I don’t even tend to allow them in that space (I’m finicky like that). I mostly use my altar as a grounding space, a place that is peaceful and that I could go to to feel connected to the gods and to the earth. I meditate in front of mine since that is the space in my home that is the most calm and the most focused.
As usual, though, it’s up to each person, not only in how they use the altar but in what they place on it. It’s also up to each to decide if an altar is a necessary item to their own spirituality.