How to introduce yourself in Hindi
You need about six lines, not a speech. Name, where you are from, what you do, and one sentence admitting you are learning. That last one does more work than the other five put together, because it turns the conversation from a test into a team effort.
1. Your name
मेरा stays masculine here whoever you are, because it agrees with नाम (name), and नाम is a masculine noun. You are not describing yourself, you are describing the name.
2. Where you are from
से means from, में means in. This is the first place the speaker's own gender shows up: रहती for a woman, रहता for a man.
3. Nice to meet you
Say it to parents, aunties, anyone older. It is the warm, safe one. No gender ending to worry about.
4. That you're learning
That second one is a dative sentence: literally "to me a little Hindi comes". Hindi handles knowing a language that way rather than with "I know". The verb agrees with हिंदी, which is feminine, so आती, whoever is speaking.
5. Asking back
6. When you lose the thread
Learn these two before you learn anything clever. The conversation only dies when you have no way to ask for a repeat.