What custard and ersa said
Look up 61.75 - it'll give you an FAA PPL issued on the basis of (and only valid when accompanied by) your EASA PPL/medical.
From that point, everything can be logged as PIC under FAA regs. ****Here is where the FAA is different from EASA: under the faa system if you are rated on the aircraft you can log the time as pic even if you are receiving instruction. Daft but true. Obviously this is not acceptable in Europe so you have two choices: separate logbooks FAA/EASA or just log it the EASA way. If you are staying in the states to do a cpl under part 61 you will need 250 hours Vs 200 under EASA. If you find a part 141 school you can do a cpl in 190 hours, definitely worth considering.