No, no, and still no.
Petra does indeed mean "large rock".
"Petros" is used in a few places in classical Greek poetry to mean stone or pebble. There are no examples of that usage in Koine prose.
Petra has feminine gender. It can't be a man's given name. To make a masculine name out of it, you have to switch it to a masculine declension, hence "Petros".
If you want to see a long list of citations from Protestant exegetes confirming this, here it is.
Well that's not entirely accurate. Greek noun gender doesn't have anything to do with the actual gender of the subject. For example, the greek word for "dog" is male gender, but there are clearly female dogs and you can clearly give a female name to a dog.
The greek word for "rock", Petra, is female noun gender, but it's used elsewhere to refer precisely to Christ:
1Co 10:4 And did all drink the same spiritual drink: for they drank of that spiritual Rock (Petra) that followed them: and that Rock (Petra) was Christ.
So it's perfectly reasonable withing the confines of the greek language to compare a male person to a female object and vice-versa.