add a dynamic member profile link structure to BuddyPress. Untested. YYMV.

gistfile1.php

<?php
// .com/my/profile/edit --> .com/members/paulgibbs/profile/edit
function maybe_redirect_all_the_things() {
	if ( ! is_user_logged_in() ) {
		return;
	}

	$request = parse_url( $_SERVER ['REQUEST_URI'] );
	if ( ! $request ) {
		return;
	}

	$request['path'] = trim( $request_path['path'], '/\\' );
	$path            = explode( '/', $request['path'] );

	// Intercept URLs starting with /my/.
	if ( array_shift( $path ) !== 'my' ) {
		return;
	}

	$new_path  = implode( '/', $path );
	$new_query = isset( $request['query'] ) ? "?{$request['query']}" : '';

	// Build the URL to redirect to.
	$new_url = sprintf(
		'%s/%s/%s',
		bp_loggedin_user_domain(),
		$new_path,
		$new_query
	);

	bp_core_redirect( esc_url_raw( $new_url ) );
	exit;
}
add_action( 'bp_template_redirect', 'maybe_redirect_all_the_things', 1 );