This is the test I made in a sandbox.
If you run the code and click the 2 buttons like this: first, back, first, back ... a few times you will see at the console that the name attribute of the target event becomes null even if it was not null the first time I pressed that button.
I also attached an image with some comments in the lower right corner to clarify the behaviour.
This is the code:
  handleSearchChange(event) {
    const target = event.target;
    const name = target.getAttribute("name");
    console.log("Test name " + name + "\n");
  }
  render() {
    return (
      <div>
        <div style={{ height: "30px", width: "30px" }}>
          <FirstSVG name="first_page" onClick={this.handleSearchChange} />
        </div>
        <div style={{ height: "30px", width: "30px" }}>
          <BackSVG name="back_page" onClick={this.handleSearchChange} />
        </div>
      </div>
    );
  }

 
     
    