Can I call myself Buddhist? Is Buddhism a religion?

You can call yourself a Buddhist if you give fair trial to the Buddhist teaching. You should have some faith the the Buddha, the Community and the Teaching unless you will not try the Dhamma.

Buddhism is not a religion in the sense that a religion accepts a higher power.

You can call yourself a Buddhist if you like, but that is just a name, much like your own. Does changing your name change who you are? Don't worry so much about what you should call yourself, just focus on studying and practicing Buddhism.

If you are not into the academic of philosophy studies, I don't think this is an important question you need answer to.But if you need to classify what Buddhism is for now,just take Buddhism as a way to help you understand yourself and the world around you.

Can I call myself Buddhist?

I'm going to quote parts of my answer on this question:

There isn't one agreed upon definition about when you are truely a Buddhist. Some people say you are a Buddhist if you consider yourself to be one, others say you need at least several years training from an acknowledged Buddhist teacher and/or have 'taken refuge' (which is a formal or informal ceremony which marks your decision to become a Buddhist).

Personally I like the view of Dzongsar Jamyang Khyentse Rinpoche who has written a book on the topic called "What Makes You Not a Buddhist":

It’s whether you agree with the four fundamental discoveries the Buddha made under the Bodhi tree, and if you do, you can call yourself a Buddhist (ref).

So yes, you can call yourself a Buddhist. Whether other Buddhists agree with you may depend on the tradition they follow.

Is Buddhism a religion?

Most Buddhists I know regard Buddhism as a lifestyle rather than a religion. However, most non-Buddhists see it as a religion, probably because it shares many aspects commonly found in a religion.

BTW, you may find that the answers on this question 'Is Buddhism a religion or a philosophy?' give more insight in this matter.

You can call yourself a Buddhist. Other people can call you a Buddhist. But it is only words. Buddha is real, Buddhism is only idea. Some respectful people can say that Buddhism is a religion, but again it is only words and ideas. If you want to go this way, go without unnecessary words.

As a zen buddhist in Florida of the United States, taking refuge in the three jewels is the ceremony in which one will often consider themselves becoming buddhist. Taking on the precepts can be seen as the threshold one makes to become a Buddhist. Afterwards one often gets a "Dharma name" and formally calls themselves a Buddhist Practitioner.

Of course this is all merely ceremonial but the point of taking on a title is very tied to ceremonies. I graduated college with a ceremony. I grew another year with a ceremony. I became a man with a ceremony. Ceromonies help define ourselves to ourselves and to others.

However in my personal experience one becomes a Buddhist when they join a sangha. It is in a sangha where I feel the practice really comes alive in my life.

I doubt you'll find a good answer as to whether Buddhism is a religion or a way of life, simply because there's a ton of stuff that's called Buddhism and not everyone agrees as to what constitutes a religion anyway.

Many Buddhists consider taking the vows to be the thing that makes you a Buddhist, so if you want to make it "official", you can take the vows at your friendly neighborhood Buddhist Temple.

Outside of that, I imagine you can call yourself a Buddhist if you believe in the Buddha and his message.

Do keep in mind that Buddhism is just a label; it's really about how you live. You need not identify yourself as a Buddhist to live a Buddhist life and many people who identify as Buddhists do not live a Buddhist life.

Buddhism has the idea of the three jewels: Buddha, Dharma, Sangha.

You said "I believe in Buddha and his philosophy" so that's two of them, i.e. Buddha, and Dharma.

There are parts e.g. in the Dhammapada which suggest it's better to be alone than with a fool:

If for company you cannot find a wise and prudent friend who leads a good life, then, like a king who leaves behind a conquered kingdom, or like a lone elephant in the elephant forest, you should go your way alone.

But Buddhism might also support (or encourage or recommend) friendship. For example, the Upaddha Sutta says,

I have heard that on one occasion the Blessed One was living among the Sakyans. Now there is a Sakyan town named Sakkara. There Ven. Ananda went to the Blessed One and, on arrival, having bowed down to the Blessed One, sat to one side. As he was sitting there, Ven. Ananda said to the Blessed One, "This is half of the holy life, lord: admirable friendship, admirable companionship, admirable camaraderie."[1]

"Don't say that, Ananda. Don't say that. Admirable friendship, admirable companionship, admirable camaraderie is actually the whole of the holy life. When a monk has admirable people as friends, companions, & comrades, he can be expected to develop & pursue the noble eightfold path.

"And how does etc.

Note: As AN 8.54 points out, this means not only associating with good people, but also learning from them and emulating their good qualities.