If I understand correctly... if you mean the next feature that has a value, then you can do this with the AttributeManager.
I just tried it on some parks data, and this is my setup:
It means that when a park name is null, then it will be given the name of the nearest park (nearest in record order, not spatially).
There were three steps to set that up:
Expand the Advanced Attribute Value Handling section and set Substitute Missing, Null and Empty to Closest Adjacent Feature
Check the box for Enable Adjacent Feature Attributes and set how many features you want to check. You said the "next" so perhaps you would leave Prior Features to zero and just set Subsequent Features. Here I chose both so I got the nearest, not necessarily the next.
Create a new attribute and set it to the value of the old attribute. Here I created NewAttr and set it to the value of ParkName.
Now you'll get the correct, non-null value in your new attribute.
The alternative was just to set ParkName to the value of ParkName. That would also have worked. So why did I put it in a new attribute? It might not be an issue for you, but I used the Prior Features option. If there was a block of records all null (say features 50-59) then feature 50 gets the value from 49, then feature 51 gets the value from 50, 52 gets it from 51, etc. In other words each null record takes its value from the one that's just been set (because that's now the closest). So feature 59 would take the value of feature 58, which traces back to feature 49, when in reality 59 is closer to 60 than 49. If I make a new attribute, then the original is not affected, and records 50-54 would get the value of 49, and 55-59 would get the value of 60.
OK, that last bit's a bit of a brain-teaser, but if you don't use the Prior Features option, and just look for subsequent features it won't be an issue. I put it just in case you meant "nearest" not "next", and for any other users who happen to have a similar issue and find this answer.
Whether I understood correctly or not, I think finding adjacent values is an interesting problem, so I put together a solution and added it to the FME Hub. You can find it here: https://hub.safe.com/publishers/safe-lab/transformers/adjacentfeaturenullattributemapper