That is fine. I wouldn't be alarmed.
Just enjoy the phone and use it like normal. If it needs to be charged everyday then that is fine. Just remember to run it down to 20% or less at least once a month and the battery will last for years.
I wonder where this myth got started because I read it a lot online. The longest life for a lithium ion battery can be achieved by partial discharges and frequent recharges as opposed to full discharges. In no way, shape or form does a full discharge/recharge extend the life of a l-ion battery. In fact, it puts additional strain on it, shortening its life. Lithium ion batteries have no memory effect like nickel cadmium, therefore there is no harm from partial recharging.