What did Paul mean by receive him as myself in Philemon?
Paul meant that Philemon should welcome Onesimus exactly as he would welcome Paul himself, extending the same partnership, acceptance, and fellowship. Onesimus was no longer merely a slave but a beloved brother in the Lord, so Paul asked Philemon to receive him as a partner and fellow believer.
Les explains that Paul was dealing with Onesimus on like ground. In verse 17, Paul says if Philemon counts him a partner, he should receive Onesimus as myself. Les puts it this way: when Onesimus shows up at Philemon's house, open the door to him like you would if it were Paul. This is a beautiful illustration of the word imputed, as seen in Romans. Onesimus had run away from his slave owner, but Paul asks Philemon to receive him back forever, no longer as a servant only, but above a servant, a brother beloved, both in the flesh and in the Lord. Then in verse 18, Paul says if Onesimus has wronged Philemon or owes anything, put that on Paul's account—impute it to him. Paul is asking Philemon not to exact it from Onesimus, since he was still just a common slave.
If thou count me therefore a partner, receive him as myself.