It is more common that a client use the same Realtor for both the buy and sell when staying in the same neighborhood. When a seller is moving to another area, it is common to have different Realtors.
There is a benefit of coordination when it is the same agent. It is certainly very workable when there are two different agents. You might have very good reason to want one person to represent you in the buy and a different agent to represent you in the sale of your property.
The real key here is the reason. If you are listed, and you call another Realtor to show you property, they might assume you will be working with your current agent and wonder why you called them. Be candid and upfront. It's very workable, and your choice.