The context is this:
Whatever you ask in my name, this I will do, that the Father may be glorified in the Son. If you ask me anything in my name, I will do it. (John 14:13-14)You did not choose me, but I chose you and appointed you that you should go and bear fruit and that your fruit should abide, so that whatever you ask the Father inmyname, he may give it to you. (John 15:16)
In that day you will ask nothing of me. Truly, truly, I say to you, whatever you ask of the Father in my name, he will give it to you. Until now you have asked nothing in my name. Ask, and you will receive, that your joy may be full…In that day you will ask in my name, and I do not say to you that I will ask the Father on your behalf; (John 16:23-24, 26)
However “in my name” actually often means “in my authority”, or “for my sake”. As in the following examples:
“Whoever receives one such child in my name receives me (Matthew18:5)“For where two or three are gathered in my name, there am I among them.” (Matthew 18:20)“For many will come in my name, saying, ‘I am the Christ,’ and they will lead many astray.” (Matthew 24:5)
So no, as long as it is understood it is possible – as in the Lord’s prayer – to not mention Jesus. But again, there is no harm and some benefit in often adding “we ask this prayer in Jesus’ name” or similar when praying on behalf of a group.
For a related subject, baptism into the name of Jesus, see Is baptism in the name of the Father, Son and Holy Spirit the same as baptism in the name of Jesus?