There are two different solfeges. Fixed do and movable do. It sounds like you use fixed do, which emanates from do always being C. Movable do supposes that do is the root of the key. Thus, if a song has do,re,mi, in fixed do, the notes are always CDE, whereas in movable do, say in Eb, the notes will be EbFG. This in itself can be confusing for a beginner.
Assuming fixed do, yes, sing the names, which are easy to do, with one syllable each. BUT - it'll become cumbersome later, when you meet sharps and flats. In Dmajor, there'll be an F#, with various names in solfege, but even singing 'F#' has two syllables. Of course, in movable do, that F# becomes mi. Using movable actually gives you a better feel of how each note relates to the others, and how it fits into the scheme of things.
Probably better in the long run to think/say/sing the note names. However, learning the piano usually has two stages when it comes to playing notes. Initially at least, one looks at the dots, thinks 'CDE', then finds C,D and E on the keys to play. This short-circuits after a while, to something like 'I just played C, next is a D that's just to the right' - obviously this goes on subconsciously, otherwise we'd never finish playing a tune!
So, if it helps for now, continue. But sooner or later, it will actually start to slow your playing down.