An easy and simple way to say this is: ぼくのねこのなまえはゆかです。 (Boku no neko no namae wa Yuka desu) Or just: ぼくのねこはゆかです。 (Boku no neko wa Yuka desu)

私は（僕は・俺は）猫の　名前が　ユカです。 Watashi wa neko no namae ga Yuka desu Watashi, is a first-person pronoun. Watashi is used by men in polite conversation, and by women all the time. Neko means cat. Namae is name. The other are all grammatical items I'm happy to explain.